Μαθηματικά Α' Δημοτικού. Τετράδιa Εργασιών. 1o και 2o τεύχοi [PDF]

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1

¶ÚÔÛ·Ó·ÙÔÏÈÛÌfi˜ ÛÙÔ ¯ÒÚÔ

1 ¶ËÁ·›Óˆ ¢ı›· Î·È ÛÙÚ›‚ˆ ‰ÂÍÈ¿. ÷ڿ˙ˆ Ì ÙÔ ÌÔχ‚È ÙË ‰È·‰ÚÔÌ‹. ΔÔ ·˘ÙÔΛÓËÙÔ ÛÙÚ›‚ÂÈ ·ÚÈÛÙÂÚ¿ ‹ ‰ÂÍÈ¿;

2 ÷ڿ˙ˆ ÌÈ· ÁÚ·ÌÌ‹, ¤ÙÛÈ ÒÛÙ ٷ ÎfiÎÎÈÓ· ÏÔ˘ÏÔ‡‰È· Ó· ‚Ú›ÛÎÔÓÙ·È Ì¤Û· ÛÙË ÁÚ·ÌÌ‹.

10

Ë

ÂÓfiÙËÙ· 1

3 μÚ›ÛΈ ÙË ‰È·‰ÚÔÌ‹ Ô˘ Ú¤ÂÈ Ó· ·ÎÔÏÔ˘ı‹ÛÂÈ ÙÔ ÔÓÙ›ÎÈ ÁÈ· Ó· ÊÙ¿ÛÂÈ ÛÙÔ Ù˘Ú›.

11

2

°ÂˆÌÂÙÚÈο Û¯‹Ì·Ù·

1 ™˘Ó‰¤ˆ Ì ÙÔÓ ›‰ÈÔ ÙÚfiÔ Î·È Ù· ˘fiÏÔÈ· Û¯‹Ì·Ù·.

2 Ãڈ̷ٛ˙ˆ Ì ÙÔ ›‰ÈÔ ¯ÚÒÌ· Ù· ÁˆÌÂÙÚÈο ÛÙÂÚ¿.

12

Ë

ÂÓfiÙËÙ· 1

3 ™˘Ó‰¤ˆ Ù· Û¯‹Ì·Ù· Ì ÙÔ fiÓÔÌ¿ ÙÔ˘˜.

TÚ›ÁˆÓÔ

·ÎÏÔ˜

ÔÚıÔÁÒÓÈÔ

ÙÂÙÚ¿ÁˆÓÔ

4 Ãڈ̷ٛ˙ˆ Ì ÙÔ ›‰ÈÔ ¯ÚÒÌ· ·˘Ù¿ Ô˘ ¤¯Ô˘Ó ÙÔ ›‰ÈÔ Û¯‹Ì·.

13

3

™‡ÁÎÚÈÛË Î·È ÂÎÙ›ÌËÛË ÔÛÔًوÓ

1 ¶·Ú·ÙËÚÒ Û οı ÂÈÎfiÓ· fiÛ· Â›Ó·È Ù· ‰¿¯Ù˘Ï·. ¢È·Áڿʈ ·fi οı ÂÈÎfiÓ· Ù· ·ÓÙÈΛÌÂÓ· Ô˘ ÂÚÈÛÛ‡ԢÓ.

2 ™˘Ó‰¤ˆ Ì ÌÈ· ÁÚ·ÌÌ‹ ÙȘ Û˘ÏÏÔÁ¤˜ Ô˘ ¤¯Ô˘Ó ›ÛÔ ·ÚÈıÌfi ·ÓÙÈÎÂÈ̤ӈÓ.

3 §¤ˆ fiÛ˜ Â›Ó·È ÔÈ ÎÔ˘ÎΛ‰Â˜.

14

Ë

ÂÓfiÙËÙ· 1

4

¶ÚÔÊÔÚÈ΋ ·Ú›ıÌËÛË.

1

2

...

10 5

™¯Â‰È¿˙ˆ ÙfiÛ˜ ÁÚ·Ì̤˜ fiÛ· Â›Ó·È Ù· ·˘ÙÔÎÈÓËÙ¿ÎÈ·.

II 6 ∑ˆÁÚ·Ê›˙ˆ ¤Ó· ΢ÎÏ¿ÎÈ ÂÚÈÛÛfiÙÂÚÔ.

∑ˆÁÚ·Ê›˙ˆ ¤Ó· ΢ÎÏ¿ÎÈ ÏÈÁfiÙÂÚÔ.

7 ¶·Ú·ÙËÚÒ ÙËÓ ÂÈÎfiÓ· Î·È Û˘Ó¯›˙ˆ Ì ÙÔÓ ›‰ÈÔ ÙÚfiÔ.

4. OÈ Ì·ıËÙ¤˜ ·ÚÈıÌÔ‡Ó ÚÔÊÔÚÈο ̤¯ÚÈ ÙÔ 10, ÍÂÎÈÓÒÓÙ·˜ ·fi ‰È¿ÊÔÚÔ˘˜ ·ÚÈıÌÔ‡˜.

15

4

OÈ ·ÚÈıÌÔ› ·fi ÙÔ 1 ¤ˆ˜ ÙÔ 5

1

¢È·‚¿˙ˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

2

4

1

3

5 2

μ¿˙ˆ Û ·ÎÏÔ ÙfiÛ· ·È¯Ó›‰È· fiÛ· ‰ËÏÒÓÂÈ Ô ·ÚÈıÌfi˜.

2 4 3 5 3 ™˘ÌÏËÚÒÓˆ ÙËÓ ÂÈÎfiÓ· Ì ٷ Ì‹Ï· Î·È ÙȘ ÎÔ˘ÎΛ‰Â˜ Ô˘ Ï›Ô˘Ó.

2 3 5 16

1. ¢Â›¯ÓÔ˘Ì ÙȘ ηÚ٤Ϙ Ì ÙÔ˘˜ ·ÚÈıÌÔ‡˜, ÙÔ˘˜ ÔÔ›Ô˘˜ ‰È·‚¿˙Ô˘Ó ÔÈ Ì·ıËÙ¤˜.

Ë

ÂÓfiÙËÙ· 1

4

¶fiÛ˜ Â›Ó·È ÔÈ ÎÔ˘ÎΛ‰Â˜;

ªÂÙÚÒ Ù· Ì·ÏfiÓÈ· Ô˘ ÎÚ·Ù¿ οı ·È‰› Î·È Û˘Ó‰¤ˆ ÙËÓ ÂÈÎfiÓ· Ì ÙÔÓ ·ÓÙ›ÛÙÔÈ¯Ô ·ÚÈıÌfi.

2

4

3

5

5

μÚ›ÛΈ fiÛ· Â›Ó·È Ù· ‰¿¯Ù˘Ï· Î·È Ù· ΢‚¿ÎÈ· Î·È Ù· Û˘Ó‰¤ˆ Ì ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

6

2 4 3 5 4. ¢Â›¯ÓÔ˘Ì ÙȘ ηÚ٤Ϙ Ì ÙȘ ÎÔ˘ÎΛ‰Â˜ Î·È ÔÈ Ì·ıËÙ¤˜ ‚Ú›ÛÎÔ˘Ó fiÛ˜ ›ӷÈ.

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5

∞Ú›ıÌËÛË, ·Ó¿ÁÓˆÛË Î·È ÁÚ·Ê‹ ÙˆÓ ·ÚÈıÌÒÓ (I) ∑ˆÁÚ·Ê›˙ˆ fiÛ˜ ÎÔ˘ÎΛ‰Â˜ Ú¤ÂÈ.

1

2 ¶·Ú·ÙËÚÒ Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi 2.

2 2 3 ¶·Ú·ÙËÚÒ ÙȘ ÂÈÎfiÓ˜ Î·È ÙȘ ÂÓÒÓˆ Ì ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

2 3 1 4 18

1. H ‰·ÛοϷ ϤÂÈ ¤Ó·Ó ·ÚÈıÌfi ̤¯ÚÈ ÙÔ 5 Î·È ÔÈ Ì·ıËÙ¤˜ ˙ˆÁÚ·Ê›˙Ô˘Ó ÙËÓ ·ÓÙ›ÛÙÔÈ¯Ë Û˘ÛÙÔȯ›· Ì ÙË ÌÔÚÊ‹ ÙÔ˘ ˙·ÚÈÔ‡.

Ë

ÂÓfiÙËÙ· 1

4 ¶·Ú·ÙËÚÒ Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi 3.

3 3 5 Ãڈ̷ٛ˙ˆ οı ÊÔÚ¿ ÙfiÛ· ΢ÎÏ¿ÎÈ· fiÛ· Â›Ó·È Ù· ·ÓÙÈΛÌÂÓ·.

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6

∞Ú›ıÌËÛË, ·Ó¿ÁÓˆÛË Î·È ÁÚ·Ê‹ ÙˆÓ ·ÚÈıÌÒÓ (II) ∞ÓÙ›ÛÙÚÔÊË ·Ú›ıÌËÛË ÍÂÎÈÓÒÓÙ·˜ ·fi ÙÔ 10.

1

10 9 8 7 6 5 4 3 2 1 2 ¶·Ú·ÙËÚÒ Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi 5.

5 5 3 ∂ÓÒÓˆ Ì ÌÈ· ÁÚ·ÌÌ‹ ÙȘ ÎÔ˘ÎΛ‰Â˜ Ì ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

20

Ë

ÂÓfiÙËÙ· 1 ¶fiÛ˜ Â›Ó·È ÔÈ ÎÔ˘ÎΛ‰Â˜;

4

5 Ãڈ̷ٛ˙ˆ ÙfiÛ˜ Ì¿Ï˜ fiÛ˜ ‰Â›¯ÓÔ˘Ó ÔÈ ·ÚÈıÌÔ›.

2 4 5 3 6 6 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

3

6 7 8 9 10

4. Δ· ·È‰È¿ ÌÂÙÚÔ‡Ó ÙȘ ÎÔ˘ÎΛ‰Â˜ Î·È Ï¤Ó fiÛ˜ ›ӷÈ.

21

7

¶ÚfiÛıÂÛË Î·È ·Ó¿Ï˘ÛË ÙˆÓ ·ÚÈıÌÒÓ Ì¤¯ÚÈ ÙÔ 5 (π)

1 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

3

2

3 1

1

4 1 2

™˘ÌÏËÚÒÓˆ ‹ ‰È·Áڿʈ ÊÚÔ‡Ù·, ÁÈ· Ó· Â›Ó·È ÙfiÛ· fiÛ· ‰ËÏÒÓÂÈ Ô ·ÚÈıÌfi˜.

5

5

4

3

3

22

4

4

2

Ë

ÂÓfiÙËÙ· 1

3

¶fiÛ˜ Â›Ó·È ÔÈ ÎÔ˘ÎΛ‰Â˜;

4 ¶·Ú·ÙËÚÒ Î·È Û˘ÌÏËÚÒÓˆ ÙȘ ÎÔ˘ÎΛ‰Â˜ Î·È ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

ηÈ

1

ηÈ

2

ηÈ

4

ηÈ

5

ηÈ

2

ηÈ

5 5

°Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

1 1

2 2

1 1

2 2

3 3

4 4

3 3

5 5

3. OÈ Ì·ıËÙ¤˜ ·Ú·ÙËÚÔ‡Ó ÙÔ˘˜ Û¯ËÌ·ÙÈÛÌÔ‡˜ Î·È Ï¤Ó ÚÔÊÔÚÈο ÙÔÓ ·ÓÙ›ÛÙÔÈ¯Ô ·ÚÈıÌfi.

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8

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ·

1

¶ÔÈÔ˜ ·ÚÈıÌfi˜ Â›Ó·È ÚÈÓ Î·È ÔÈÔ˜ ÌÂÙ¿;

3

4

5

... 2

¶fiÛ· Â›Ó·È fiÏ· οı ÊÔÚ¿;

ηÈ

Î·È ŸÏ· ›ӷÈ

ŸÏ· Â›Ó·È Î·È

ŸÏ· ›ӷÈ

1

1

ηÈ

2

ŸÏ· ›ӷÈ

3 μ¿˙ˆ Û ·ÎÏÔ fiÏ· Ù· ÔÚıÔÁÒÓÈ· Î·È ¯ÚˆÌ·Ù›˙ˆ ·˘Ùfi Ô˘ Â›Ó·È ›‰ÈÔ Ì ÙÔ ÚfiÙ˘Ô.

¶ÚfiÙ˘Ô

24

1. §¤Ì ÛÙ· ·È‰È¿ ¤Ó·Ó ·ÚÈıÌfi ·fi ÙÔ 1 ̤¯ÚÈ ÙÔ 10 Î·È ÙÔ˘˜ ˙ËÙԇ̠ӷ Ì·˜ Ô˘Ó ÙÔÓ ÚÔËÁÔ‡ÌÂÓÔ Î·È ÙÔÓ ÂfiÌÂÓÔ ·ÚÈıÌfi.

Ë

ÂÓfiÙËÙ· 1

4

∑ˆÁÚ·Ê›˙ˆ ÎÔ˘ÎΛ‰Â˜.

5 ªÔÈÚ¿˙ˆ ÙȘ ηڷ̤Ϙ Û ‰‡Ô ̤ÚË Ì ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜. ™˘ÌÏËÚÒÓˆ Ù· ÎÔ˘Ù¿ÎÈ· Ì ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

5

ηÈ

Î·È Î·È

ηÈ

ηÈ

6 Ãڈ̷ٛ˙ˆ Ì ÙÔ ›‰ÈÔ ¯ÚÒÌ· Ù· ·ÓÙ›ÛÙÔȯ· Û¯‹Ì·Ù·.

4. ∏ ‰·ÛοϷ ϤÂÈ ¤Ó·Ó ·ÚÈıÌfi ̤¯ÚÈ ÙÔ 5 Î·È ÔÈ Ì·ıËÙ¤˜ ˙ˆÁÚ·Ê›˙Ô˘Ó ÙËÓ ·ÓÙ›ÛÙÔÈ¯Ë Û˘ÛÙÔȯ›· Ì ÙË ÌÔÚÊ‹ ÙÔ˘ ˙·ÚÈÔ‡.

25

9

™‡ÁÎÚÈÛË ÌÂÁÂıÒÓ

1 °Ú¿Êˆ ·ÚÈıÌÔ‡˜ ÁÈ· Ó· ÌÔ˘Ó ÛÙË ÛÂÈÚ¿ Ù· ·ÓÙÈΛÌÂÓ· ·fi ÙÔ ÈÔ Ì·ÎÚ‡ ˆ˜ ÙÔ ÈÔ ÎÔÓÙfi.

1

°Ú¿Êˆ ·ÚÈıÌÔ‡˜ ÁÈ· Ó· ÌÔ˘Ó ÛÙË ÛÂÈÚ¿ Ù· ‚È‚Ï›· ·fi ÙÔ ÈÔ Ï·Ù‡ ̤¯ÚÈ ÙÔ ÈÔ ÛÙÂÓfi.

°Ú¿Êˆ ·ÚÈıÌÔ‡˜ ÁÈ· Ó· ÌÔ˘Ó ÛÙË ÛÂÈÚ¿ Ù· Û΢ÏÈ¿ ·fi ÙÔ ÈÔ ¯ÔÓÙÚfi ˆ˜ ÙÔ ÈÔ ÏÂÙfi.

26

Ë

ÂÓfiÙËÙ· 2

2

A

B

°

¢

¶ÔÈÔ ÔÚıÔÁÒÓÈÔ Â›Ó·È: ÙÔ ÈÔ „ËÏfi; .....

ÙÔ ÈÔ ¯·ÌËÏfi; .....

ÙÔ ÈÔ Ï·Ù‡; .....

ÙÔ ÈÔ ÛÙÂÓfi; .....

3 ∑ˆÁÚ·Ê›˙ˆ ¤Ó· Ê›‰È ÈÔ Ì·ÎÚ‡ Î·È ÈÔ ¯ÔÓÙÚfi.

∑ˆÁÚ·Ê›˙ˆ ¤Ó· ÎÔ˘Ù› ÈÔ Ï·Ù‡ Î·È ÈÔ „ËÏfi.

∑ˆÁÚ·Ê›˙ˆ ¤Ó· ÎÔ˘Ù› ÈÔ ÛÙÂÓfi Î·È ÈÔ ¯·ÌËÏfi ·fi ÙÔ ·Ú¯ÈÎfi.

27

10

OÈ ·ÚÈıÌÔ› ·fi ÙÔ 6 ̤¯ÚÈ ÙÔ 10 (π)

¶fiÛ· Â›Ó·È fiÏ· Ù· „¿ÚÈ·; ¶Ò˜ ¯ˆÚ›˙ÔÓÙ·È ÌÂٷ͇ ÙÔ˘˜; °Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

ŸÏ· Ì·˙› ›ӷÈ

Èڛ˙ÔÓÙ·È ÛÂ

Èڛ˙ÔÓÙ·È ÛÂ

ηÈ

ηÈ

1

2

¶·Ú·ÙËÚÒ Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi 8.

8 ¶fiÛ· Â›Ó·È fiÏ· Ù· ‰ÂÏÊ›ÓÈ·; ¶Ò˜ ¯ˆÚ›˙ÔÓÙ·È ÌÂٷ͇ ÙÔ˘˜; °Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

ŸÏ· Ì·˙› ›ӷÈ

28

Èڛ˙ÔÓÙ·È ÛÂ

Èڛ˙ÔÓÙ·È ÛÂ

ηÈ

ηÈ

3

Ë

ÂÓfiÙËÙ· 2

4 μÚ›ÛΈ fiÛ· Â›Ó·È fiÏ· Ù· ˙Ò· Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi. Ãڈ̷ٛ˙ˆ fiÛ· ΢ÎÏ¿ÎÈ· Ú¤ÂÈ.

6

5 ¶·Ú·ÙËÚÒ ÙȘ ÂÈÎfiÓ˜ Î·È ÙȘ ÂÓÒÓˆ Ì ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

6

8

7

5

29

11

OÈ ·ÚÈıÌÔ› ·fi ÙÔ 6 ̤¯ÚÈ ÙÔ 10 (ππ)

1 ¶·Ú·ÙËÚÒ Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi 9.

9 9 2 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó. Ãڈ̷ٛ˙ˆ ÙfiÛ· ÙÂÙÚ¿ÁˆÓ· fiÛ· ‰ËÏÒÓÂÈ Ô ·ÓÙ›ÛÙÔȯԘ ·ÚÈıÌfi˜.

0 30

1

2

5

Ë

ÂÓfiÙËÙ· 2

3

°Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ ·ÎÔ‡ˆ.

4 ªÔÈÚ¿˙ˆ Ù· Û¯‹Ì·Ù· Û ‰‡Ô ̤ÚË Ì ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜ Î·È Ù· ۯ‰ȿ˙ˆ. ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

10

9

5

ηÈ

4

5

ηÈ

5

Î·È Î·È Î·È Î·È Î·È

ηÈ

ηÈ

3. ∏ ‰·ÛοϷ ˘·ÁÔÚ‡ÂÈ ÌÂ Ù˘¯·›· ÛÂÈÚ¿ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ ·fi ÙÔ 4 ¤ˆ˜ ÙÔ 10, ÙÔ˘˜ ÔÔ›Ô˘˜ ÁÚ¿ÊÔ˘Ó ÔÈ Ì·ıËÙ¤˜.

ηÈ

ηÈ

31

12

™‡ÁÎÚÈÛË ·ÚÈıÌÒÓ – Δ· ۇ̂ÔÏ· =, > ηÈ


3 ™˘ÌÏËÚÒÓˆ ÙȘ ϤÍÂȘ Î·È ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

4

2

¤Ó· ÙÚ›·

5 32

1. §¤Ì ÛÙ· ·È‰È¿ ¤Ó·Ó ·ÚÈıÌfi ·fi ÙÔ 1 ̤¯ÚÈ ÙÔ 10 Î·È ÙÔ˘˜ ˙ËÙԇ̠ӷ Ì·˜ Ô˘Ó ÙÔÓ ÚÔËÁÔ‡ÌÂÓÔ Î·È ÙÔÓ ÂfiÌÂÓÔ ·ÚÈıÌfi.

Ë

ÂÓfiÙËÙ· 2

2

μÚ›ÛΈ ·ÚÈıÌÔ‡˜ ÌÂÁ·Ï‡ÙÂÚÔ˘˜ Î·È ÌÈÎÚfiÙÂÚÔ˘˜ ·fi ·˘ÙfiÓ.

4

5

7

4

9 5

∑ˆÁÚ·Ê›˙ˆ „¿ÚÈ· Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

>

=

>


… 6=…

6

2 …

9, < ‹ =.

5>3

6 ... 6

9 ... 8 + 1 1 + 0 ... 10

7 ... 9

8 ... 10

9 ... 6

2 + 2 ... 4 + 1 4

™˘Ó¯›˙ˆ Ì ÙÔÓ ›‰ÈÔ ÙÚfiÔ.

678 40

678

6 1. ¶ÚÔÙ›ÓÔ˘Ì ·ıÚÔ›ÛÌ·Ù· ‰‡Ô ·ÚÈıÌÒÓ Ì¤¯ÚÈ ÙÔ 5.

Ë

ÂÓfiÙËÙ· 2

5 ªÔÈÚ¿˙ˆ Ù· ÊÔÚÙËÁ¿ Û ‰‡Ô ̤ÚË Ì ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜. °Ú¿Êˆ ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

8

+

+

+

+ + 6

ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

3 + 2 ...

4 + 1 ...

1+2+0+1= ... 2 + ... = 3

1 1 + 2 ...

3 1 + 0 ...

2 + ... 5

1+3+1+0= ... 1+1+1+1+0= ...

0 + ... = 2

4 + ... = 4

... + 3 = 5 41

ªÂ ·fiÊ·ÛË Ù˘ ∂ÏÏËÓÈ΋˜ ∫˘‚¤ÚÓËÛ˘ Ù· ‰È‰·ÎÙÈο ‚È‚Ï›· ÙÔ˘ ¢ËÌÔÙÈÎÔ‡, ÙÔ˘ °˘ÌÓ·Û›Ô˘ Î·È ÙÔ˘ §˘Î›Ԣ Ù˘ÒÓÔÓÙ·È ·fi ÙÔÓ √ÚÁ·ÓÈÛÌfi ∂ΉfiÛˆ˜ ¢È‰·ÎÙÈÎÒÓ μÈ‚Ï›ˆÓ Î·È ‰È·Ó¤ÌÔÓÙ·È ‰ˆÚÂ¿Ó ÛÙ· ¢ËÌfiÛÈ· ™¯ÔÏ›·. Δ· ‚È‚Ï›· ÌÔÚ› Ó· ‰È·Ù›ıÂÓÙ·È ÚÔ˜ ÒÏËÛË, fiÙ·Ó Ê¤ÚÔ˘Ó ‚È‚ÏÈfiÛËÌÔ ÚÔ˜ ·fi‰ÂÈÍË Ù˘ ÁÓËÛÈfiÙËÙ¿˜ ÙÔ˘˜. ∫¿ı ·ÓÙ›Ù˘Ô Ô˘ ‰È·Ù›ıÂÙ·È ÚÔ˜ ÒÏËÛË Î·È ‰Â ʤÚÂÈ ‚È‚ÏÈfiÛËÌÔ, ıˆÚÂ›Ù·È ÎÏ„›Ù˘Ô Î·È Ô ·Ú·‚¿Ù˘ ‰ÈÒÎÂÙ·È Û‡Ìʈӷ Ì ÙȘ ‰È·Ù¿ÍÂȘ ÙÔ˘ ¿ÚıÚÔ˘ 7, ÙÔ˘ ¡fiÌÔ˘ 1129 Ù˘ 15/21 ª·ÚÙ›Ô˘ 1946 (ºEK 1946, 108, Aã).

BIB§IO™HMO

∞·ÁÔÚ‡ÂÙ·È Ë ·Ó··Ú·ÁˆÁ‹ ÔÔÈÔ˘‰‹ÔÙ ÙÌ‹Ì·ÙÔ˜ ·˘ÙÔ‡ ÙÔ˘ ‚È‚Ï›Ô˘, Ô˘ ηχÙÂÙ·È ·fi ‰ÈηÈÒÌ·Ù· (copyright), ‹ Ë ¯Ú‹ÛË ÙÔ˘ Û ÔÔÈ·‰‹ÔÙ ÌÔÚÊ‹, ¯ˆÚ›˜ ÙË ÁÚ·Ù‹ ¿‰ÂÈ· ÙÔ˘ ¶·È‰·ÁˆÁÈÎÔ‡ πÓÛÙÈÙÔ‡ÙÔ˘.

17

OÈ ·ÚÈıÌÔ› ·fi ÙÔ 10 ̤¯ÚÈ ÙÔ 20

1

¢È·‚¿˙ˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

14

17

12

16

19

13

20 2

K¿ı ̷ıËÙ‹˜ ı· ¤¯ÂÈ Ì›· ÙÛ¿ÓÙ·;

3 ªÂÙÚÒ Î·È ‚¿˙ˆ Û ·ÎÏÔ ÙÔ ÛˆÛÙfi ·ÚÈıÌfi.

16

17 10

18 17 19 18

1. OÈ Ì·ıËÙ¤˜ ‰È·‚¿˙Ô˘Ó ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ ‚Ú›ÛÎÔÓÙ·È Û οı Ï·›ÛÈÔ.

Ë

ÂÓfiÙËÙ· 3

4 ∏ Ì›· ηڷ̤Ϸ ÎÔÛÙ›˙ÂÈ 1 ÏÂÙfi.

1 ÏÂÙfi

O ¶˘ı·ÁfiÚ·˜: ñ ÃÚÂÈ¿˙ÂÙ·È

ÏÂÙ¿ ÁÈ· Ó· ·ÁÔÚ¿ÛÂÈ

ÙȘ Ú¿ÛÈÓ˜ ηڷ̤Ϙ. ñ XÚÂÈ¿˙ÂÙ·È

ÏÂÙ¿ ÁÈ· Ó· ·ÁÔÚ¿ÛÂÈ

ÙȘ ÎfiÎÎÈÓ˜ ηڷ̤Ϙ. ñ ÃÚÂÈ¿˙ÂÙ·È

ÏÂÙ¿ ÁÈ· Ó· ·ÁÔÚ¿ÛÂÈ

fiϘ ÙȘ ηڷ̤Ϙ.

5 ™˘ÌÏËÚÒÓˆ ÙȘ ϤÍÂȘ Î·È ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

‰¤Î·

7

6 Ìˉ¤Ó

9

8 11

18

∞ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10

1 O ¶¤ÙÚÔ˜ ›¯Â 7 ·˘ÙÔÎÈÓËÙ¿ÎÈ·. ∞ÁfiÚ·ÛÂ

·ÎfiÌ·. ¶fiÛ· ·˘ÙÔÎÈÓËÙ¿ÎÈ· ¤¯ÂÈ ÙÒÚ·;

... + ... = ... OÈ Î·ÛÂÙ›Ó˜ ¤¯Ô˘Ó ̤۷ ÌÔχ‚È·. ¶fiÛ· Â›Ó·È fiÏ· Ù· ÌÔχ‚È· Ì·˙›;

5

5 + 4 = ....

4

7

7 + 3 = ...

3 2

ÀÔÏÔÁ›˙ˆ Ù· ·ıÚÔ›ÛÌ·Ù·.

12

5 + 2 = ...

6 + 3 = ...

5 + 4 = ...

9 + 1 = ...

8 + 2 = ...

6 + 4 = ...

Ë

ÂÓfiÙËÙ· 3 ÀÔÏÔÁ›˙ˆ ·ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10.

¶fiÛ· Â›Ó·È fiÏ·; ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ıÚÔ›ÛÌ·Ù·.

... + ... = ...

3

4

.....................

4

6

.....................

..................... 5

ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ Ù· ·ıÚÔ›ÛÌ·Ù·.

4 + 2 = ...

7 + 3 = ...

6 + 3 = ...

2 + 4 = ...

3 + 7 = ...

3 + 6 = ...

2 + 8 = ...

5 + 4 = ...

7 + 2 = ...

8 + 2 = ...

4 + 5 = ...

2 + 7 = ...

3. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ ¤Ó· ¿ıÚÔÈÛÌ· ̤¯ÚÈ ÙÔ 10. OÈ Ì·ıËÙ¤˜ ˘ÔÏÔÁ›˙Ô˘Ó ÓÔÂÚ¿ ÙÔ ¿ıÚÔÈÛÌ· Î·È ÙÔ ÁÚ¿ÊÔ˘Ó Ì ÙË ¯Ú‹ÛË Û˘Ì‚fiÏˆÓ Ì¤Û· ÛÙÔ Ï·›ÛÈÔ.

13

19

T·ÎÙÈÎÔ› ·ÚÈıÌÔ› – Δ· ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù·

1

¶ÚÔÊÔÚÈ΋ ·Ú›ıÌËÛË ÙˆÓ Ù·ÎÙÈÎÒÓ ·ÚÈıÌÒÓ.

2Ô˜

1Ô˜

...

10Ô˜ 2

ΔÔ Êȉ¿ÎÈ

™¯Â‰›·Û ÙÔ ·ÓÙÈΛÌÂÓÔ ÛÙÔ ÔÔ›Ô ¤ÊÙ·ÛÂ Ô ¶˘ı·ÁfiÚ·˜.

∏ À·Ù›· ¤ÊÙ·Û ÛÙÔ

ΔÈ ·ÚÈıÌfi ¤Ù˘¯Â Ì ٷ ˙¿ÚÈ·; °Ú¿Êˆ ÙÔÓ ·ÚÈıÌfi Ù˘ ı¤Û˘ ÛÙËÓ ÔÔ›· ‚Ú›ÛÎÂÙ·È Î¿ı ÂÈÎfiÓ·.

2Ô

3 ∂ÓÒÓˆ ÌÂ ÌÈ· ÁÚ·ÌÌ‹ ÙÔ ÛˆÛÙfi ¿ıÚÔÈÛÌ·.

1+1 1 14

2

2+2

3+3

4+4

5+5

3

5

7

9 10

4

6

8

1. ∑ËÙԇ̠·fi ÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ··ÁÁ›ÏÔ˘Ó ÙÔ˘˜ Ù·ÎÙÈÎÔ‡˜ ·ÚÈıÌÔ‡˜ ̤¯ÚÈ ÙÔ 10.

Ë

ÂÓfiÙËÙ· 3

4

¢ÈÏ¿ ·ıÚÔ›ÛÌ·Ù·

5

ΔÔ ÌÈÛfi

μ¿˙ˆ Û ·ÎÏÔ Ù· ÌÈÛ¿. °Ú¿Êˆ fiÛ· Â›Ó·È Ù· ÌÈÛ¿.

2

6 μ¿˙ˆ Û ·ÎÏÔ Ù· ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù·.

3+1=4

2+2=4

6+2 =8

6+1=7

1+1=2

2+3=5

5+3=8

3+3=6

1+4=5

4+4=8

5 + 5 = 10

7+2=9

4. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10. OÈ Ì·ıËÙ¤˜ ˘ÔÏÔÁ›˙Ô˘Ó ÓÔÂÚ¿ Ù· ·ıÚÔ›ÛÌ·Ù· Î·È Ù· ÁÚ¿ÊÔ˘Ó Ì ÙË ¯Ú‹ÛË Û˘Ì‚fiÏˆÓ Ì¤Û· ÛÙ· Ï·›ÛÈ·.

15

20

Δ· ÓÔÌ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10

1 ¶ÔÈÔ˜ ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ ÙÔ ·ÚÎÔ˘‰¿ÎÈ;

8ú

∏ À·Ù›· ¤¯ÂÈ ... ∂Àƒø.

O ¡›ÎÔ˜ ¤¯ÂÈ ... ∂Àƒø.

∏ ∫ÔÚ›Ó· ¤¯ÂÈ ... ∂Àƒø. ΔÔ ·ÚÎÔ˘‰¿ÎÈ ÌÔÚ› Ó· ÙÔ ·ÁÔÚ¿ÛÂÈ ............

2 ∏ À·Ù›· ¤¯ÂÈ 9 ∂Àƒø. μ¿˙ˆ Û ·ÎÏÔ ÙÔ ÔÚÙÔÊfiÏÈ Ù˘.

16

Ë

ÂÓfiÙËÙ· 3 ÀÔÏÔÁ›˙ˆ ·ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10.

μ¿˙ˆ Û ·ÎÏÔ ÙÔ ÔÚÙÔÊfiÏÈ Ô˘ ı· ¿ÚÂÈ Ô ¶˘ı·ÁfiÚ·˜.

3

4

O ¶˘ı·ÁfiÚ·˜ ı¤ÏÂÈ Ó· ·ÓÙ·ÏÏ¿ÍÂÈ Ù· ÓÔÌ›ÛÌ·Ù¿ ÙÔ˘ Ì ÓÔÌ›ÛÌ·Ù· ÙÔ˘ ÂÓfi˜ ÏÂÙÔ‡.

∏ NfiË ¤¯ÂÈ 6 ú. ™¯Â‰È¿˙ˆ Ù· ÓÔÌ›ÛÌ·Ù· Û ∂Àƒø Ô˘ ÌÔÚ› Ó· ¤¯ÂÈ.

O £·Ó¿Û˘ ¤¯ÂÈ 10 ú. ™¯Â‰È¿˙ˆ Ù· ÓÔÌ›ÛÌ·Ù· Û ∂Àƒø Ô˘ ÌÔÚ› Ó· ¤¯ÂÈ.

3. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ ·ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10. OÈ Ì·ıËÙ¤˜ ˘ÔÏÔÁ›˙Ô˘Ó ÓÔÂÚ¿ οı ÊÔÚ¿ ÙÔ ¿ıÚÔÈÛÌ· Î·È ÙÔ ÁÚ¿ÊÔ˘Ó Ì ÙË ¯Ú‹ÛË Û˘Ì‚fiÏˆÓ Ì¤Û· ÛÙÔ Ï·›ÛÈÔ.

5

17

21

¶ÚÔÛıÂÙÈ΋ ·Ó¿Ï˘ÛË ·ÚÈıÌÒÓ ·fi ÙÔ 6 ̤¯ÚÈ ÙÔ 10 YÔÏÔÁ›˙ˆ Ù· ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù·.

1

2 H EϤÓË ı¤ÏÂÈ Ó· ÙÔÔıÂÙ‹ÛÂÈ Ù· ‚È‚Ï›· Û ‰‡Ô Ú¿ÊÈ· ÛÙË ‚È‚ÏÈÔı‹ÎË Ù˘ ·‰ÂÏÊ‹˜ Ù˘. AÓ ¤¯ÂÈ 6 ‚È‚Ï›·, Ì fiÛÔ˘˜ ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜ ÌÔÚ› Ó· Ù· ÙÔÔıÂÙ‹ÛÂÈ ÛÙ· Ú¿ÊÈ·;

6+0=6 5+1=6 ... + ... = ... + ... = ... + ... = ... + ... = ... + ... =

AÓ ¤¯ÂÈ 7 ‚È‚Ï›·, Ì fiÛÔ˘˜ ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜ ÌÔÚ› Ó· Ù· ÙÔÔıÂÙ‹ÛÂÈ ÛÙ· Ú¿ÊÈ·;

7+0=7 6+1=7 ... + ... = ... + ... = ... + ... = ... + ... = ... + ... = ... + ... =

18

AÓ ¤¯ÂÈ 8 ‚È‚Ï›·, Ì fiÛÔ˘˜ ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜ ÌÔÚ› Ó· Ù· ÙÔÔıÂÙ‹ÛÂÈ ÛÙ· Ú¿ÊÈ·;

8+0=8 7+1=8 ... + ... = ... + ... = ... + ... = ... + ... = ... + ... = ... + ... = ... + ... =

1. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ ·ıÚÔ›ÛÌ·Ù· Ù˘ ÌÔÚÊ‹˜ Ó + Ó, ‰ËÏ·‰‹ 1 + 1, 2 + 2, 3 + 3, 4 + 4 Î·È 5 + 5.

Ë

ÂÓfiÙËÙ· 3

3 Aӷχˆ Ì ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜ ÙÔÓ ·ÚÈıÌfi 9 Û ¿ıÚÔÈÛÌ·.

0+9 1+8

9

4 YÔÏÔÁ›˙ˆ Ù· ·ıÚÔ›ÛÌ·Ù·.

5 + 2 = ...

4 + 4 = ...

5 + 5 = ...

4 + 3 = ...

4 + 6 = ...

8 + 2 = ...

6 + 2 = ...

5 + 3 = ...

5 + 4 = ...

7 + 3 = ...

3 + 6 = ...

2 + 7 = ... 19

22

¶ÚÔ‚Ï‹Ì·Ù·

1

¶fiÛ˜ ηڤÎϘ ı· ¯ÚÂÈ·ÛÙԇ̠·ÎfiÌ· ÁÈ· Ó· ηı›ÛÔ˘Ó 10 ηÏÂṲ̂ÓÔÈ;

10 2

¢¤Î· Ó¿ÓÔÈ Ì¤ÓÔ˘Ó Û ‰‡Ô ÛÈÙ¿ÎÈ·. μÚ›ÛΈ fiÏÔ˘˜ ÙÔ˘˜ ÙÚfiÔ˘˜ Ì ÙÔ˘˜ ÔÔ›Ô˘˜ Â›Ó·È ‰˘Ó·ÙfiÓ Ó· ÌÔÈÚ·ÛÙÔ‡Ó ÛÙ· ‰‡Ô ÛÈÙ¿ÎÈ·.

0 + + + + + + 20

= = = = = =

10 10 10 10 10 10

+ + + + +

= = = = =

10 10 10 10 10

Ë

ÂÓfiÙËÙ· 3

3 ¶fiÛ˜ ÂÙ·ÏÔ‡‰Â˜ Ú¤ÂÈ Ó· ÂÙ¿ÍÔ˘Ó ·fi ÙÔ ÎfiÎÎÈÓÔ ÛÙÔ Î›ÙÚÈÓÔ ÏÔ˘ÏÔ‡‰È, ¤ÙÛÈ ÒÛÙ ٷ ‰‡Ô ÏÔ˘ÏÔ‡‰È· Ó· ¤¯Ô˘Ó ÙÔÓ ›‰ÈÔ ·ÚÈıÌfi ÂÙ·ÏÔ‡‰ˆÓ;

4 ºÙÈ¿¯Óˆ ¤Ó· ‰ÈÎfi ÌÔ˘ Úfi‚ÏËÌ· Î·È ÙÔ Ï‡Óˆ.

21

23

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ·

1

ÀÔÏÔÁ›˙ˆ ·ıÚÔ›ÛÌ·Ù· ÌÂ ÙÔÓ ·ÚÈıÌfi 5.

2 Δ· 10 Ô˘ÏÈ¿ ı· ηı›ÛÔ˘Ó ÛÙ· ‰‡Ô ‰¤ÓÙÚ·. ªÂ fiÛÔ˘˜ ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜ ÌÔÚÔ‡Ó Ó· ηı›ÛÔ˘Ó; ™˘ÌÏËÚÒÓˆ Ù· ·ıÚÔ›ÛÌ·Ù·:

0 + 10 = 10 ... + ... = 10 ... + ... = ... ... + ... = ... ... + ... = ... ... + ... = ...

... + ... = ... ... + ... = ... ... + ... = ... ... + ... = ... ... + ... = ...

√È ÛÔÎÔÏ¿Ù˜ ∫¿ı ÛÔÎÔÏ¿Ù· ¤¯ÂÈ 10 ÎÔÌÌ¿ÙÈ·. ¶fiÛ· ÎÔÌÌ¿ÙÈ· ÛÔÎÔÏ¿Ù·˜ ˘¿Ú¯Ô˘Ó Û οı ÂÚ›ÙˆÛË;

13

22

1. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ ·ıÚÔ›ÛÌ·Ù· Ù˘ ÌÔÚÊ‹˜ 5 + Ó, ‰ËÏ·‰‹ 5 + 1, 5 + 2, 5 + 3, 5 + 4 Î·È 5 + 5.

3

Ë

ÂÓfiÙËÙ· 3 ¶ÚÔÊÔÚÈ΋ ·Ú›ıÌËÛË ÙˆÓ Ù·ÎÙÈÎÒÓ ·ÚÈıÌÒÓ.

1Ô˜

2Ô˜

4

10Ô˜ 5

¶ÔÈÔ˜ ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ ÙÔ ·È¯Ó›‰È;

9ú

∏ ª·Ú›· ¤¯ÂÈ ... ∂Àƒø

O Ã·Û¿Ó ¤¯ÂÈ ... ∂Àƒø.

∏ ÕÚÙÂÌË ¤¯ÂÈ ... ∂Àƒø. ΔÔ ·È¯Ó›‰È ÌÔÚ› Ó· ÙÔ ·ÁÔÚ¿ÛÂÈ ..............

6 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ Ù· ·ıÚÔ›ÛÌ·Ù·.

3 + 3 = ... 5 + 2 = ...

7 + 3 = ... 4 + 4 = ...

5 + 5 = ... 8 + 2 = ...

6 + 4 = ...

5 + 3 = ...

4 + 5 = ...

4. ∑ËÙԇ̠·fi ÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ··ÁÁ›ÏÔ˘Ó ÙÔ˘˜ Ù·ÎÙÈÎÔ‡˜ ·ÚÈıÌÔ‡˜ ̤¯ÚÈ ÙÔ 10.

23

25

OÈ ·ÚÈıÌÔ› ̤¯ÚÈ ÙÔ 50

μÚ›ÛΈ ÙÔÓ ÚÔËÁÔ‡ÌÂÓÔ Î·È ÙÔÓ ÂfiÌÂÓÔ ·ÚÈıÌfi ηıÒ˜ Î·È ÙË ‰Âο‰·.

20

1

40

30

2 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

10

‰¤Î·

¤Ó‰Âη

‰Ò‰Âη

‰ÂηÙÚ›·

‰Âη٤ÛÛÂÚ·

‰Âη¤ÓÙÂ

‰Âη¤ÍÈ

‰ÂηÂÙ¿

‰ÂηÔÎÙÒ

‰ÂηÂÓÓ¤·

›ÎÔÛÈ

3 °Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ ÁÈ· Ó· Û˘ÌÏËÚˆıÔ‡Ó ÔÈ ÛÂÈÚ¤˜.

22

25

27

36

37

48 45 4

¶·Ú·ÙËÚÒ Î·È Û˘Ó¯›˙ˆ.

5 10 30 35 10 20 3 6 24

15

... ... ...

... ... ... ...

... 50 ... ...

...

...

...

21

...

...

50

1. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ ·ÚÈıÌÔ‡˜ ̤¯ÚÈ ÙÔ 50 Î·È ·˘ÙÔ› ‚Ú›ÛÎÔ˘Ó ÙÔÓ ÂfiÌÂÓÔ Î·È ÙÔÓ ÚÔËÁÔ‡ÌÂÓÔ ·ÚÈıÌfi. ∂›Û˘ ÚÔÙ›ÓÔ˘Ì ÛÙÚÔÁÁ˘Ï¤˜ ‰Âο‰Â˜ (.¯. 30) Î·È ÔÈ Ì·ıËÙ¤˜ ‚Ú›ÛÎÔ˘Ó ÙËÓ ÂfiÌÂÓË Î·È ÙËÓ ÚÔËÁÔ‡ÌÂÓË ‰Âο‰· (40, 20).

Ë

ÂÓfiÙËÙ· 4

5

ªÂÙÚÒ ·Ó¿ 5 ̤¯ÚÈ ÙÔ 50.

5

50 6 ªÂÙÚÒ Ù· ΢‚¿ÎÈ· Î·È ˘ÔÏÔÁ›˙ˆ ÙÔ ¿ıÚÔÈÛÌ¿ Ùo˘˜. ŸÏ· ›ӷÈ

10+ 5

...........

ŸÏ· ›ӷÈ

...........

ŸÏ· ›ӷÈ

7 ªÂÙÚÒ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

5. Δ· ·È‰È¿ ÌÂÙÚÔ‡Ó ·Ó¿ 5 ̤¯ÚÈ ÙÔ 50. ™ÙË Û˘Ó¤¯ÂÈ· ÁÚ¿ÊÔ˘Ó ÙÔ˘˜ ·ÚÈıÌÔ‡˜ ̤۷ ÛÙ· ΢ÎÏÈο Ï·›ÛÈ·.

25

26

X¿Ú·ÍË ÁÚ·ÌÌÒÓ

1 X·Ú¿˙ˆ ÙȘ ÁÚ·Ì̤˜ Ì ÙÔ ¯¿Ú·Î· ÁÈ· Ó· Û¯ËÌ·Ù›Ûˆ ÙÔ ÛÈÙ¿ÎÈ.

2 ™˘ÌÏËÚÒÓˆ ÙÔ ¯ÚÈÛÙÔ˘ÁÂÓÓÈ¿ÙÈÎÔ ‰¤ÓÙÚÔ.

26

Ë

ÂÓfiÙËÙ· 4

3 ™¯Â‰È¿˙ˆ Ù· ÂÚÈÁÚ¿ÌÌ·Ù·.

™˘Ó¯›˙ˆ ÙË ÁÚ·ÌÌ‹.

4 ™˘ÌÏËÚÒÓˆ ÙËÓ Î¿Ùˆ ÂÈÎfiÓ· ÒÛÙ ӷ Â›Ó·È ›‰È· Ì ÙËÓ Â¿Óˆ.

27

27

ªÔÙ›‚·

1 ™˘Ó¯›˙ˆ ÙÔ ¯ÚˆÌ·ÙÈÛÌfi Ì ÙÔÓ ›‰ÈÔ ÙÚfiÔ.

™˘Ó¯›˙ˆ ÙË ¯¿Ú·ÍË Ù˘ ÁÚ·ÌÌ‹˜ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ ¯ÚˆÌ·ÙÈÛÌfi.

2 ™¯Â‰È¿˙ˆ Ù· ›‰È· Û¯‹Ì·Ù·.

28

Ë

ÂÓfiÙËÙ· 4

3 ÷ڿ˙ˆ ÙËÓ ÌÏ ÁÚ·ÌÌ‹ Î·È ¤ÂÈÙ· ÙËÓ ÎfiÎÎÈÓË.

™˘Ó¯›˙ˆ ÙË ¯¿Ú·ÍË ÙˆÓ ÁÚ·ÌÌÒÓ Ì ÙÔÓ ›‰ÈÔ ÙÚfiÔ.

4 ¢ËÌÈÔ˘ÚÁÒ ‰Èο ÌÔ˘ ÌÔÙ›‚·.

29

28

∞Ê·›ÚÂÛË Ì ·Ê·ÈÚÂÙ¤Ô ÌÈÎÚfi ·ÚÈıÌfi

1

∞ÚÈıÌÒ ·ÓÙ›ÛÙÚÔÊ· ÍÂÎÈÓÒÓÙ·˜ ·fi ÙÔ 20.

20

19

18

...

1 2

ΔÔ Î·Ï¿ıÈ Â›¯Â 10 ηÚfiÙ·. ΔÔ ÎÔ˘Ó¤ÏÈ ¤Ê·Á 3 ηÚfiÙ·. ¶fiÛ· ηÚfiÙ· ¤ÌÂÈÓ·Ó Ì¤Û· ÛÙÔ Î·Ï¿ıÈ;

... – ... = ...

10

O ªÂӤϷԘ ›¯Â 8 ÁÚ·ÌÌ·ÙfiÛËÌ· ÛÙË Û˘ÏÏÔÁ‹ ÙÔ˘. Œ‰ˆÛÂ

ÁÚ·ÌÌ·ÙfiÛËÌ· ÛÙÔÓ ¡›ÎÔ. ¶fiÛ· ÁÚ·ÌÌ·ÙfiÛËÌ· ¤¯ÂÈ ÙÒÚ·;

... – ... = ... 30

1. OÈ Ì·ıËÙ¤˜ ·ÚÈıÌÔ‡Ó ÚÔÊÔÚÈο ·ÓÙ›ÛÙÚÔÊ· ÍÂÎÈÓÒÓÙ·˜ ·fi ÙÔÓ ·ÚÈıÌfi 20.

Ë

ÂÓfiÙËÙ· 4

3 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ ÛÙȘ ÈÛfiÙËÙ˜.

5 – 2 = ...

... – ... = ...

... – ... = ...

... – ... = ...

... – ... = ...

... – ... = ... 4

ÀÔÏÔÁ›˙ˆ ÙȘ Ú¿ÍÂȘ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

4 – 1 = ...

3 – 1 = ...

7 – 1 = ...

3 + 1 = ...

2 + 1 = ...

6 + 1 = ...

5 – 3 = ...

6 – 1 = ...

4 – 2 = ...

2 + 3 = ...

5 + 1 = ...

2 + 2 = ... 31

29

¢È¿ÎÚÈÛË ÙˆÓ Û˘Ì‚fiÏˆÓ (+) Î·È (–)

1 °Ú¿Êˆ ÙȘ ÛˆÛÙ¤˜ Ú¿ÍÂȘ ̤۷ ÛÙ· ¤Ù·Ï· ÙˆÓ ÏÔ˘ÏÔ˘‰ÈÒÓ.

7–1 4+1

4+1 5

7–2 4+2 2+3 8–2

6

3+3 8–3

μ¿Êˆ Ù· Ì·ÏfiÓÈ· Ì ÙÔ ¯ÚÒÌ· Ô˘ Ù·ÈÚÈ¿˙ÂÈ.

3+2

2+2

5–1

6–2

6–1

3+3

5+1

4 5

32

6

2

Ë

ÂÓfiÙËÙ· 4

°Ú¿Êˆ ÙȘ ÚÔÛı¤ÛÂȘ Î·È ÙȘ ·Ê·ÈÚ¤ÛÂȘ Î·È ˘ÔÏÔÁ›˙ˆ Ù· ·ÔÙÂϤÛÌ·Ù·.

3

4 §‡Óˆ Ù· ÚÔ‚Ï‹Ì·Ù· Î·È Áڿʈ ÙȘ Ú¿ÍÂȘ. Œ¯ˆ 5 ú Î·È ·ÁÔÚ¿˙ˆ ÌÈ· ÛÔÎÔÏ¿Ù· ŸÏ· Ù· ÎÂÚÈ¿ ‹Ù·Ó 4. ŒÛ‚ËÛ·Ó Ô˘ ÎÔÛÙ›˙ÂÈ 2 ú. ¶fiÛ· Ú¤ÛÙ· ı· ¿Úˆ; Ù· 3. ¶fiÛ· ÎÂÚÈ¿ ̤ÓÔ˘Ó ·Ó·Ì̤ӷ;

2ú °Ú¿Êˆ ÙËÓ Ú¿ÍË:

°Ú¿Êˆ ÙËÓ Ú¿ÍË:

5 ∞fi ÙËÓ ÚfiÛıÂÛË ‚Ú›ÛΈ ÙȘ ‰‡Ô ·Ê·ÈÚ¤ÛÂȘ.

3+2=5

5–3=2

4+2=6

5–2=3

3+1=4

4+3=7

3. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ ÚÔ‚Ï‹Ì·Ù· ÚfiÛıÂÛ˘ Î·È ·Ê·›ÚÂÛ˘. OÈ Ì·ıËÙ¤˜ ÁÚ¿ÊÔ˘Ó ÙȘ Ú¿ÍÂȘ Î·È ÙÔ ·ÔÙ¤ÏÂÛÌ·.

33

30

∞Ê·›ÚÂÛË Ì ·Ê·ÈÚÂÙ¤Ô ÌÂÁ¿ÏÔ ·ÚÈıÌfi

1

ªÂÙÚÒ ·Ó¿ 2.

2

4

6

...

20 2

ª¤Û· ÛÙÔ ÎÔ˘Ù› ˘¿Ú¯Ô˘Ó 7 ‚fiÏÔÈ. μÁ¿˙Ô˘Ì ÙÔ˘˜ 5. ¶fiÛÔÈ ‚fiÏÔÈ ¤ÌÂÈÓ·Ó;

7

–

= 3

∞fi ÙËÓ ÚfiÛıÂÛË ‚Ú›ÛΈ ÙȘ ‰‡Ô ·Ê·ÈÚ¤ÛÂȘ.

6 + 4 = 10

10– 4 = ...

6+2=8

10– 6 = ...

5+4=9

34

5+2=7

1. Δ· ·È‰È¿ ·ÚÈıÌÔ‡Ó ·Ó¿ 2 ̤¯ÚÈ ÙÔ 20.

Ë

ÂÓfiÙËÙ· 4

4 ■ Δ· Úfi‚·Ù· Â›Ó·È ...... ■ Δ· ÁÔ˘ÚÔ‡ÓÈ· Â›Ó·È ...... ■ Δ· Úfi‚·Ù· Â›Ó·È ...... ÂÚÈÛÛfiÙÂÚ·.

... – ... = ... 5 ¢È·Ù˘ÒÓˆ ¤Ó· ‰ÈÎfi ÌÔ˘ Úfi‚ÏËÌ·.

10 – 8 = ... 9 – 7 = ...

6 – 5 = ... 6

ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙȘ ·Ú·Î¿Ùˆ Ú¿ÍÂȘ.

7 + 3 = ... 10 – 5 = ...

5 + 3 = ...

10 – 7 = ...

1 + 7 = ...

8 – 5 = ...

5 + 5 = ...

8 – 7 = ...

8 – 3 = ... 35

31

ΔÔ Û˘Ìϋڈ̷

1

ÀÔÏÔÁ›˙ˆ ÙÔ Û˘Ìϋڈ̷ ÙÔ˘ ·ÚÈıÌÔ‡ 10.

2 Ãڈ̷ٛ˙ˆ Ì ÎfiÎÎÈÓÔ ¯ÚÒÌ· Ù· Ì·ÏfiÓÈ· Ô˘ ¤¯Ô˘Ó ¿ıÚÔÈÛÌ· ›ÛÔ Ì 10.

9+1

4+6

8+2

4+5

5+5

7+2

6+3

3+7

10 3 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

3 6

5 9

36

4

10

1

2 1

7

10

1. ∏ ‰·ÛοϷ ϤÂÈ Î¿ı ÊÔÚ¿ ¤Ó·Ó ·ÚÈıÌfi Î·È ÚˆÙ¿ ÙÔ˘˜ Ì·ıËÙ¤˜ fiÛ· ¯ÚÂÈ¿˙ÔÓÙ·È ·ÎfiÌË ÁÈ· Ó· Á›ÓÔ˘Ó 10. OÈ Ì·ıËÙ¤˜ ÁÚ¿ÊÔ˘Ó Û οı Ï·›ÛÈÔ ÙÔ ÛˆÛÙfi ¿ıÚÔÈÛÌ· (.¯. 8 + 2).

Ë

ÂÓfiÙËÙ· 4

4

∏ À·Ù›· ¤¯ÂÈ ÃÚÂÈ¿˙ÂÙ·È ·ÎfiÌ·

∂Àƒø. ∂Àƒø

10 ¢ÚÒ

ÁÈ· Ó· ·ÁÔÚ¿ÛÂÈ ÙÔ ‚È‚Ï›Ô.

5 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

10– 2 = ...

4 + ... = 7 10– 7 = ...

10– 5 = ... 10– 4 = ...

8 – 6 = ...

7 – 5 = ... 10– 9 = ... 7 + ... = 10 5 + ... = 10

5 + ... = 9

7 + ... = 9 37

32

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ· ∞ÚÈıÌÒ ·ÓÙ›ÛÙÚÔÊ· ÍÂÎÈÓÒÓÙ·˜ ·fi ÙÔ 20.

20

19

18

...

1

1 2

™˘Ó¯›˙ˆ ÙË ¯¿Ú·ÍË ÙˆÓ ÁÚ·ÌÌÒÓ Ì ÙÔ ¯¿Ú·Î·.

™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

38

1. OÈ Ì·ıËÙ¤˜ ·ÚÈıÌÔ‡Ó ÚÔÊÔÚÈο ·ÓÙ›ÛÙÚÔÊ· ÍÂÎÈÓÒÓÙ·˜ ·fi ÙÔÓ ·ÚÈıÌfi 20.

3

Ë

ÂÓfiÙËÙ· 4 ÀÔÏÔÁ›˙ˆ ÙÔ Û˘Ìϋڈ̷ ÙÔ˘ ·ÚÈıÌÔ‡ 10.

4

5 ∞fi ÙËÓ ÚfiÛıÂÛË ‚Ú›ÛΈ ÙȘ ‰‡Ô ·Ê·ÈÚ¤ÛÂȘ.

8 + 2 = 10

10– 2 = ...

6+3=9

10– 8 = ...

4+3=7

7 + 3 = 10

6 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

8 – 2 = ...

7 – 3 = ... 10– 2 = ...

5 – 1 = ... 10– 4 = ...

9 – 7 = ...

9 – 3 = ...

8 – 6 = ...

10– 2 = ...

7 + ... = 9 8 + ... = 10 4 + ... = 10 4. ∏ ‰·ÛοϷ ϤÂÈ Î¿ı ÊÔÚ¿ ¤Ó·Ó ·ÚÈıÌfi Î·È ÚˆÙ¿ ÙÔ˘˜ Ì·ıËÙ¤˜ fiÛ· ¯ÚÂÈ¿˙ÔÓÙ·È ·ÎfiÌË ÁÈ· Ó· Á›ÓÔ˘Ó 10. OÈ Ì·ıËÙ¤˜ ÁÚ¿ÊÔ˘Ó Û οı Ï·›ÛÈÔ ÙÔ ÛˆÛÙfi ¿ıÚÔÈÛÌ· (.¯. 6 + 4 = 10).

39

ªÂ ·fiÊ·ÛË Ù˘ ∂ÏÏËÓÈ΋˜ ∫˘‚¤ÚÓËÛ˘ Ù· ‰È‰·ÎÙÈο ‚È‚Ï›· ÙÔ˘ ¢ËÌÔÙÈÎÔ‡, ÙÔ˘ °˘ÌÓ·Û›Ô˘ Î·È ÙÔ˘ §˘Î›Ԣ Ù˘ÒÓÔÓÙ·È ·fi ÙÔÓ √ÚÁ·ÓÈÛÌfi ∂ΉfiÛˆ˜ ¢È‰·ÎÙÈÎÒÓ μÈ‚Ï›ˆÓ Î·È ‰È·Ó¤ÌÔÓÙ·È ‰ˆÚÂ¿Ó ÛÙ· ¢ËÌfiÛÈ· ™¯ÔÏ›·. Δ· ‚È‚Ï›· ÌÔÚ› Ó· ‰È·Ù›ıÂÓÙ·È ÚÔ˜ ÒÏËÛË, fiÙ·Ó Ê¤ÚÔ˘Ó ‚È‚ÏÈfiÛËÌÔ ÚÔ˜ ·fi‰ÂÈÍË Ù˘ ÁÓËÛÈfiÙËÙ¿˜ ÙÔ˘˜. ∫¿ı ·ÓÙ›Ù˘Ô Ô˘ ‰È·Ù›ıÂÙ·È ÚÔ˜ ÒÏËÛË Î·È ‰Â ʤÚÂÈ ‚È‚ÏÈfiÛËÌÔ, ıˆÚÂ›Ù·È ÎÏ„›Ù˘Ô Î·È Ô ·Ú·‚¿Ù˘ ‰ÈÒÎÂÙ·È Û‡Ìʈӷ Ì ÙȘ ‰È·Ù¿ÍÂȘ ÙÔ˘ ¿ÚıÚÔ˘ 7, ÙÔ˘ ¡fiÌÔ˘ 1129 Ù˘ 15/21 ª·ÚÙ›Ô˘ 1946 (ºEK 1946, 108, Aã).

BIB§IO™HMO

∞·ÁÔÚ‡ÂÙ·È Ë ·Ó··Ú·ÁˆÁ‹ ÔÔÈÔ˘‰‹ÔÙ ÙÌ‹Ì·ÙÔ˜ ·˘ÙÔ‡ ÙÔ˘ ‚È‚Ï›Ô˘, Ô˘ ηχÙÂÙ·È ·fi ‰ÈηÈÒÌ·Ù· (copyright), ‹ Ë ¯Ú‹ÛË ÙÔ˘ Û ÔÔÈ·‰‹ÔÙ ÌÔÚÊ‹, ¯ˆÚ›˜ ÙË ÁÚ·Ù‹ ¿‰ÂÈ· ÙÔ˘ ¶·È‰·ÁˆÁÈÎÔ‡ πÓÛÙÈÙÔ‡ÙÔ˘.

33

OÚÁ¿ÓˆÛË Û˘ÏÏÔÁÒÓ – ∞ÚÈıÌÔ› ̤¯ÚÈ ÙÔ 50

1

ÀÔÏÔÁ›˙ˆ ·ıÚÔ›ÛÌ·Ù· Ì ‰Âο‰Â˜.

2 ªÂÙÚÒ Ù· ΢‚¿ÎÈ· Î·È ˘ÔÏÔÁ›˙ˆ Ùo ¿ıÚoÈÛÌ¿ ÙÔ˘˜.

10

10+ 3

ŸÏ· ›ӷÈ

..................

ŸÏ· ›ӷÈ

..................

ŸÏ· ›ӷÈ

..................

ŸÏ· ›ӷÈ

1. ¶ÚÔÙ›ÓÔ˘Ì ·ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 50 ÛÙ· ÔÔ›· Â·Ó·Ï·Ì‚¿ÓÂÙ·È ÙÔ 10 (.¯. 10 + 10 + 10 + 7). ¶ÚÔÙ›ÓÔ˘Ì Â›Û˘ ·ıÚÔ›ÛÌ·Ù· ÛÙ· ÔÔ›· Û ¤Ó·Ó ·ÚÈıÌfi ÛÙÚÔÁÁ˘ÏÒÓ ‰Âο‰ˆÓ (10, 20, 30, 40) ÚÔÛı¤ÙÔ˘Ì ÙÔ 10 (.¯. 30 + 10).

Ë

ÂÓfiÙËÙ· 5

3 ¶fiÛ· ÏÂÙ¿ ¤¯ÂÈ Î¿ı ·È‰›;

™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

10+ 10 + ... = ...

.......................... = ...

.......................... = ... 4 μÚ›ÛΈ Ù· ·ıÚÔ›ÛÌ·Ù·.

10+ 4 = ...

10+ 9 = ...

10+ 10+ 3 = ...

10+ 10+ 1= ...

10+10+10+ 6 = ... 10+10+10+ 7 = ... 11

34

ªÔÓ¿‰Â˜ Î·È ‰Âο‰Â˜ (I)

1 ¶fiÛ· Â›Ó·È Î¿ı ÊÔÚ¿ Ù· ÌÔχ‚È· Î·È Ù· ÙÂÙÚ·ÁˆÓ¿ÎÈ·; μ¿˙ˆ Û ·ÎÏÔ ÙÔ ÛˆÛÙfi ·ÚÈıÌfi.

23

32

14

41

35

53

45

54 2

™˘ÌÏËÚÒÓˆ ÙÔÓ ÂӉȿÌÂÛÔ ·ÚÈıÌfi.

21, ..., 23

19, ..., 21

39, ..., 41

29, ..., 31

36, ..., 38

49, ..., 51 3

°Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ì ϤÍÂȘ.

11 22 36 12

12 29 44

18 33 50

Ë

ÂÓfiÙËÙ· 5 ™¯ËÌ·Ù›˙ˆ Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi.

4

5 °Ú¿Êˆ ÙÔ ·ÔÙ¤ÏÂÛÌ· ÙˆÓ ڿ͈Ó. ¶·ÚÔ˘ÛÈ¿˙ˆ ÙȘ Ú¿ÍÂȘ Î·È Ì ϤÍÂȘ. ∞Ó ¯ÚÂÈ·ÛÙ›, ¯ÚËÛÈÌÔÔÈÒ ÙÔ ·ÚÈıÌËÙ‹ÚÈÔ.

10+ 7 = 17

‰¤Î· Î·È ÂÙ¿ = ‰ÂηÂÙ¿

10+ 9 = ... ........................ = ........................ 30 + 5 = ... ........................ = ........................ 14 – 4 = 10 ‰Âη٤ÛÛÂÚ· ‚Á¿˙ˆ Ù¤ÛÛÂÚ· = ‰¤Î·

16 – 6 = ... ........................ = ........................ 28 – 8 = ... ........................ = ........................ 4. ∏ ‰·ÛοϷ ϤÂÈ ÚÔÊÔÚÈο ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÙȘ ‰Âο‰Â˜ Î·È ÙȘ ÌÔÓ¿‰Â˜ ÂÓfi˜ ·ÚÈıÌÔ‡ Î·È ÔÈ Ì·ıËÙ¤˜ ‚Ú›ÛÎÔ˘Ó ÔÈÔ˜ Â›Ó·È Ô ·ÚÈıÌfi˜ Î·È ÙÔÓ ÁÚ¿ÊÔ˘Ó ÛÙÔ Ï·›ÛÈÔ.

13

35

∞ıÚÔ›ÛÌ·Ù· Ì ÔÏÏÔ‡˜ fiÚÔ˘˜

1 ™˘ÌÏËÚÒÓˆ ÙȘ ÙÚÂȘ οÚÙ˜ ÁÈ· Ó· ¤¯ˆ ¿ıÚÔÈÛÌ· ›ÛÔ Ì 8.

8 2

1

4

3

2

3 2

™˘ÌÏËÚÒÓˆ ÙȘ ÙÚÂȘ οÚÙ˜ ÁÈ· Ó· ¤¯ˆ ¿ıÚÔÈÛÌ· ›ÛÔ Ì 10.

10 7

1

3

4

2

2 3

ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

2 + 4 + 3 = ... 4 + 1+ 5 = ... 3 + 2 + ... = 10 6 + 1+ ... = 9 14

7 +2 1 ...

2 +3 2 ...

5 +1 ... 10

Ë

ÂÓfiÙËÙ· 5

4

ÀÔÏÔÁ›˙ˆ ·ıÚÔ›ÛÌ·Ù· Ì ÙÚÂȘ ÚÔÛıÂÙ¤Ô˘˜.

5

OÈ ÓÈÊ¿‰Â˜ ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

9

3

1

1 7

1

2 2

10

8

4

3

6 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

4 +2 + 1 + 2 = ...

8 +... = 10

5 +... = 10

6 + 1 + 2 + 1 = ...

6 +... = 9

5 +2 + 3 + 1 = ...

2 +2 + 2 + 2 = ...

6 +4 + 2 = ...

4. ¶ÚÔÙ›ÓÔ˘Ì ·ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10 Ì ÙÚÂȘ ÚÔÛıÂÙ¤Ô˘˜, ÂÎ ÙˆÓ ÔÔ›ˆÓ ÔÈ ‰‡Ô Ú¤ÂÈ Ó· Â›Ó·È fiÌÔÈÔÈ, ‰ËÏ·‰‹ Ù· ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù· (Ó+Ó), Î·È Ô ÙÚ›ÙÔ˜ ÙÔ 1 ‹ ÙÔ 2 (.¯. 2 + 2 + 1, 4 + 4 + 1 Î.Ï.).

15

36

K›ÓËÛË Û ÙÂÙÚ·ÁˆÓÈṲ̂ÓÔ ¯·ÚÙ›

™¯Â‰È¿˙ˆ ÛÙÔ ‰ÂÍÈfi Û¯¤‰ÈÔ fi,ÙÈ ·ÎÚÈ‚Ò˜ ‚Ϥˆ ÛÙÔ ·ÚÈÛÙÂÚfi.

™¯Â‰È¿˙ˆ Ì ÙÔ ¯¿Ú·Î· ÙÔ ÛÈÙ¿ÎÈ ÛÙÔ ‰ÈÏ·Ófi Û¯¤‰ÈÔ.

™ÙÔ ‰ÈÏ·Ófi Û¯¤‰ÈÔ Ì·˘Ú›˙ˆ ÙÂÙÚ¿ÁˆÓ· ÛÙȘ ›‰È˜ ı¤ÛÂȘ Ì ·˘Ù¤˜ Ô˘ ‚Ϥˆ ·ÚÈÛÙÂÚ¿.

16

1

2

3

Ë

ÂÓfiÙËÙ· 5

4

°Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

5 ™¯Â‰È¿˙ˆ ÙË ‰È·‰ÚÔÌ‹ Û‡Ìʈӷ Ì ÙȘ Ô‰ËÁ›Â˜ ÁÈ· Ó· ‚ÚÂÈ ÙÔ ·È‰› ÙÔ ·ÁˆÙfi.

1

ÚÔ˜ Ù· Â¿Óˆ

2

ÚÔ˜ Ù· ‰ÂÍÈ¿

3

ÚÔ˜ Ù· Â¿Óˆ

4

ÚÔ˜ Ù· ·ÚÈÛÙÂÚ¿

T¤ÏÔ˜

AÚ¯‹

6 EÓÒÓˆ Ì ÙË ÛÂÈÚ¿ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

4. H ‰·ÛοϷ ÚÔÙ›ÓÂÈ ‰È„‹ÊÈÔ˘˜ ·ÚÈıÌÔ‡˜ ̤¯ÚÈ ÙÔ 20, ÙÔ˘˜ ÔÔ›Ô˘˜ ÔÈ Ì·ıËÙ¤˜ ÁÚ¿ÊÔ˘Ó ÛÙ· Ï·›ÛÈ·.

17

37

¶ÚÔ‚Ï‹Ì·Ù·

1 ∏ ΢ڛ· ª·Ú›· ¤ÊÙÈ·Í 10 ÁÏ˘Î¿. ™Â οı ·È‰› ı· ‰ÒÛÂÈ ·fi 2 ÁÏ˘Î¿.

¶fiÛ· ÁÏ˘Î¿ ı· ‰ÒÛÂÈ Û fiÏ· Ù· ·È‰È¿ Ì·˙›; ........ ¶fiÛ· ÁÏ˘Î¿ ı· Ù˘ Ì›ÓÔ˘Ó; ........

2 ΔÔ ÓËÛ› ÙÔ˘ 10

™ÙÔ ÓËÛ› ÙÔ˘ 10 ÙÔ ‚·ÙÚ·¯¿ÎÈ ÊÙ¿ÓÂÈ ¿ÓÙ· ˉÒÓÙ·˜ 10 ‚ÔÙÛ·Ï¿ÎÈ·. ■ ∞Ó Â›Ó·È ÛÙÔ ‚ÔÙÛ·Ï¿ÎÈ 5, Ú¤ÂÈ Ó· ˉ‹ÍÂÈ

3

■ ∞Ó Â›Ó·È ÛÙÔ ‚ÔÙÛ·Ï¿ÎÈ 2,

2

Ú¤ÂÈ Ó· ˉ‹ÍÂÈ

1

‚ÔÙÛ·Ï¿ÎÈ·.

■ ∞Ó Â›Ó·È ÛÙÔ ‚ÔÙÛ·Ï¿ÎÈ 7, Ú¤ÂÈ Ó· ˉ‹ÍÂÈ

18

‚ÔÙÛ·Ï¿ÎÈ·.

‚ÔÙÛ·Ï¿ÎÈ·.

Ë

ÂÓfiÙËÙ· 5

3 ¢È·Ù˘ÒÓˆ ‰Èο ÌÔ˘ ÚÔ‚Ï‹Ì·Ù· Û‡Ìʈӷ Ì ÙȘ ÂÈÎfiÓ˜.

..........................................................

..........................................................

..........................................................

..........................................................

..........................................................

..........................................................

..........................................................

..........................................................

4

8 ηڷ̤Ϙ

O ªÂϤÙ˘ Î·È Ë ∫ÔÚ›Ó· ÌÔÈÚ¿˙ÔÓÙ·È ÙÔ ·Î¤ÙÔ Ì ÙȘ ηڷ̤Ϙ. O ηı¤Ó·˜ ı· ¿ÚÂÈ ÙfiÛ˜ ηڷ̤Ϙ fiÛ˜ Î·È Ô ¿ÏÏÔ˜.

O ηı¤Ó·˜ ı· ¿ÚÂÈ ..... ηڷ̤Ϙ.

19

38

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ·

1

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ıÚÔ›ÛÌ·Ù·.

2

™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Î·È ÙËÓ Ú¿ÍË. À¿Ú¯Ô˘Ó Î·È Î·È °Ú¿Êˆ ÙËÓ Ú¿ÍË:

ŸÏ· Ì·˙› ›ӷÈ

3 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

5 +2 1 2 + 4 + 2 + 1 = ... 2 + ... = 10 ... 5 + ... = 9 4 7 + 2 + 1 = ... +1 ... 3 + 3 + ... = 10 3 + ... = 10 10 3 +2 + 3 + 1 = ... 3 +... = 6

20

4 +3 2 ... 4 +4 ... ...

1. ¶ÚÔÙ›ÓÔ˘Ì ·ıÚÔ›ÛÌ·Ù· ̤¯ÚÈ ÙÔ 10 Ì ÙÚÂȘ ÚÔÛıÂÙ¤Ô˘˜.

Ë

ÂÓfiÙËÙ· 5 ÀÔÏÔÁ›˙ˆ ÙÔ ¿ıÚÔÈÛÌ· ÙˆÓ ‰Âο‰ˆÓ Î·È ÙˆÓ ÌÔÓ¿‰ˆÓ ÂÓfi˜ ·ÚÈıÌÔ‡.

4

5 °Ú¿Êˆ Î·È Ï¤ˆ fiÛ˜ Â›Ó·È ÔÈ ‰Âο‰Â˜ Î·È ÔÈ ÌÔÓ¿‰Â˜. OÓÔÌ¿˙ˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ ÚÔ·ÙÔ˘Ó.

MÔÓ¿‰Â˜

MÔÓ¿‰Â˜

MÔÓ¿‰Â˜

¢Âο‰Â˜

¢Âο‰Â˜

¢Âο‰Â˜

6 ªÂÙÚÒ Î·È ‚Ú›ÛΈ ÙÔ ¿ıÚÔÈÛÌ·.

10+ –– + –– + –– =

10+ –– + –– + –– + –– =

4. ¶ÚÔÙ›ÓÔ˘Ì ·ıÚÔ›ÛÌ·Ù· Ù˘ ÌÔÚÊ‹˜ 10+Ó, 20+Ó Î.Ï., fiÔ˘ Ó ÌÔÓÔ„‹ÊÈÔ˜ ·ÚÈıÌfi˜.

21

39

ªÔÓ¿‰Â˜ Î·È ‰Âο‰Â˜ (II)

1

∞Ê·ÈÚÒ ÙȘ ÌÔÓ¿‰Â˜ ·fi ‰È„‹ÊÈÔ ·ÚÈıÌfi.

μ¿˙ˆ Û ·ÎÏÔ Ù· ÓÔÌ›ÛÌ·Ù· Ô˘ ¯ÚÂÈ¿˙ÔÓÙ·È.

2

13 ÏÂÙ¿

34 ÏÂÙ¿

48 ÏÂÙ¿

3 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó. °Ú¿Êˆ ÙȘ ‰Âο‰Â˜ Ì ÎfiÎÎÈÓÔ ¯ÚÒÌ·.

0 1 2 3 10 12 21 23 40 22

51

42

34 54

5 7 15 16 27 46

9 38

29

49 58 59

1. ¶ÚÔÙ›ÓÔ˘Ì ·Ê·ÈÚ¤ÛÂȘ Ù˘ ÌÔÚÊ‹˜ 1Ó–Ó, 2Ó–Ó Î.Ï., fiÔ˘ Ó Ô ·ÚÈıÌfi˜ Ô˘ Â›Ó·È ›ÛÔ˜ Ì ÙÔ „ËÊ›Ô ÙˆÓ ÌÔÓ¿‰ˆÓ ÙÔ˘ ‰È„‹ÊÈÔ˘ ·ÚÈıÌÔ‡.

Ë

ÂÓfiÙËÙ· 6

4 μÚ›ÛΈ ÙȘ ‰Âο‰Â˜ Î·È ÙȘ ÌÔÓ¿‰Â˜. ™˘ÌÏËÚÒÓˆ ÙȘ ÈÛfiÙËÙ˜.

ΔÔ 12 ¤¯ÂÈ ….. ‰Âο‰Â˜ Î·È ….. ÌÔÓ¿‰Â˜.

10+ 2 12 = ...................…..

ΔÔ 29 ¤¯ÂÈ ….........................................

29 = ........................

ΔÔ 33 ¤¯ÂÈ ….........................................

33 = ........................

5 μÚ›ÛΈ ÙÔ ·ÔÙ¤ÏÂÛÌ· ÙˆÓ ڿ͈Ó. ¶·ÚÔ˘ÛÈ¿˙ˆ ÙȘ Ú¿ÍÂȘ Î·È Ì ϤÍÂȘ.

10+ 2 = ... ‰¤Î· Î·È ........................ = ........................ 20 + 6 = ... ........................ = ........................ 28 – 8 = ... ........................ = ........................ 34 – 4 = ... ........................ = ........................ 6 ™˘ÌÏËÚÒÓˆ ÙȘ ÈÛfiÙËÙ˜.

10 + 9 = ... 17 – 7 = ... 10 + 10 + 4 = ... 10 + ... = 16 12 – 2 = ... 25 = ... + ... + ... 8 + 8 = ...

7 + 5 = ... 13 – ... = 10

7 + 7 = ... 18 – ... = 10 37 = ... + ... + ... + ... 23

40

°ÂˆÌÂÙÚÈο Û¯‹Ì·Ù·

1

μ¿˙ˆ Û ·ÎÏÔ Ù· Û¯‹Ì·Ù· Ô˘ ÌÔÈ¿˙Ô˘Ó. ªÂÙÚÒ fiÛ· Â›Ó·È Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi.

3

ÛÊ·›Ú˜

·‚ÔÈ

·ÏÈÓ‰ÚÔÈ

ÛÙÂÚ¿ ÔÚıÔÁÒÓÈ· 24

Ë

ÂÓfiÙËÙ· 6

2 Ãڈ̷ٛ˙ˆ Ì ÙÔ ›‰ÈÔ ¯ÚÒÌ· ·˘Ù¿ Ô˘ ÌÔÈ¿˙Ô˘Ó.

3 ªÂÙÚÒ Ù· Û¯‹Ì·Ù· Ô˘ ÌÔÈ¿˙Ô˘Ó ÌÂٷ͇ ÙÔ˘˜ Î·È Áڿʈ ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜. Y¿Ú¯Ô˘Ó

Y¿Ú¯Ô˘Ó Y¿Ú¯Ô˘Ó Y¿Ú¯Ô˘Ó

Y¿Ú¯Ô˘Ó

Y¿Ú¯Ô˘Ó 25

41

O ¯ÚfiÓÔ˜

1 μ¿˙ˆ ·ÚÈıÌÔ‡˜ ÛÙȘ ÂÈÎfiÓ˜ ÁÈ· Ó· ‰Â›Íˆ ÙË ¯ÚÔÓÈ΋ ÛÂÈÚ¿ ÙÔ˘˜.

1 2 μ¿˙ˆ ·ÚÈıÌÔ‡˜ ÛÙȘ Ë̤Ú˜ Ù˘ ‚‰ÔÌ¿‰·˜ Û‡Ìʈӷ Ì ÙË ¯ÚÔÓÈ΋ ÛÂÈÚ¿ ÙÔ˘˜.

TÚ›ÙË ¶·Ú·Û΢‹

1

K˘Úȷ΋

¶¤ÌÙË

¢Â˘Ù¤Ú·

TÂÙ¿ÚÙË

™¿‚‚·ÙÔ

3 ∑ˆÁÚ·Ê›˙ˆ ÎÂÚ¿ÎÈ· ÛÙËÓ ÙÔ‡ÚÙ· ÁÈ· Ó· ‰Â›Íˆ ÙËÓ ËÏÈΛ· ÌÔ˘.

26

Ë

ÂÓfiÙËÙ· 6

4

μ¿˙ˆ ·ÚÈıÌÔ‡˜ ÛÙȘ ÂÈÎfiÓ˜ οı ÈÛÙÔÚ›·˜ ÁÈ· Ó· ‰Â›Íˆ ÙË ¯ÚÔÓÈ΋ ÛÂÈÚ¿ ÙÔ˘˜.

1

2

5 ¶·Ú·ÙËÚԇ̠ÙËÓ ÂÈÎfiÓ· Î·È Û˘˙ËÙ¿ÌÂ.

∞ÁÒÓ·˜ ‰ÚfiÌÔ˘ ÕÓÓ·

ŒÏÏË

T›Ó·

¶ÔÈÔ ÎÔÚ›ÙÛÈ ¯ÚÂÈ¿˙ÂÙ·È ÏÈÁfiÙÂÚÔ ¯ÚfiÓÔ ÁÈ· Ó· ÊÙ¿ÛÂÈ ÛÙÔ Ù¤ÚÌ·; 27

42

¶ÚÔÛı¤ÛÂȘ Ì ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙÔ Û˘Ìϋڈ̷ ÌÔÓÔ„‹ÊÈˆÓ ·ÚÈıÌÒÓ.

1

2 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

9+5=

7+6=

+5

+6

9

7 +1

10

+4

10

8+7=

9+8=

+7 8

9 10

28

+8

10

1. H ‰·ÛοϷ ÚÔÙ›ÓÂÈ ÛÙÔ˘˜ Ì·ıËÙ¤˜ ·Û΋ÛÂȘ Û˘ÌÏËÚÒÌ·ÙÔ˜ ÌÔÓÔ„‹ÊÈˆÓ ·ÚÈıÌÒÓ (.¯. «3 Î·È fiÛÔ Ì·˜ οÓÂÈ 7;»).

Ë

ÂÓfiÙËÙ· 6 ÀÔÏÔÁ›˙ˆ ·ıÚÔ›ÛÌ·Ù· Ì ÙËÓ ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜.

3

4 ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

10

4 2

10 6

ŸÏ· Ì·˙› Â›Ó·È 20.

5 5

ŸÏ· Ì·˙› Â›Ó·È 30.

5

5

ŸÏ· Ì·˙› Â›Ó·È 18.

10

5

ŸÏ· Ì·˙› Â›Ó·È 17.

5 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ ·ÔÙ¤ÏÂÛÌ·.

8 + 3 = ...

7 + 4 = ...

9 + 7 = ...

9 + 6 = ...

8 + 4 = ...

3 + 9 = ...

2 + 9 = ...

8 + 5 = ...

8 + 8 = ...

3. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ Î¿ı ÊÔÚ¿ ¤Ó· ¿ıÚÔÈÛÌ· (.¯. 9 + 6, 8 + 4, Î.Ï.). OÈ Ì·ıËÙ¤˜ ˘ÔÏÔÁ›˙Ô˘Ó ÓÔÂÚ¿ Î·È ·ÚÔ˘ÛÈ¿˙Ô˘Ó ÚÔÊÔÚÈο ÙÔÓ ÙÚfiÔ Ì ÙÔÓ ÔÔ›Ô ˘ÔÏfiÁÈÛ·Ó.

29

43

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ·

ÀÔÏÔÁ›˙ˆ ·ıÚÔ›ÛÌ·Ù· Ì ÙËÓ ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜.

1

2 ™˘ÌÏËÚÒÓˆ Ù· ËÌÂÚÔÏfiÁÈ·.

¯ı˜

Û‹ÌÂÚ·

·‡ÚÈÔ

TÂÙ¿ÚÙË

................................

................................

...

...

7

O Ù·¯˘‰ÚfiÌÔ˜ ª¤Û· ÛÙÔ Û¿ÎÔ ÌÔ˘ ¤¯ˆ 9 ÌÈÎÚÔ‡˜ ʷΤÏÔ˘˜ Î·È 7 ÌÂÁ¿ÏÔ˘˜ ʷΤÏÔ˘˜. ¶fiÛÔÈ Â›Ó·È fiÏÔÈ ÔÈ Ê¿ÎÂÏÔÈ Ì·˙›;

30

1. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ Î¿ı ÊÔÚ¿ ¤Ó· ¿ıÚÔÈÛÌ· (.¯. 9 + 4, 8 + 3 Î.Ï.). OÈ Ì·ıËÙ¤˜ ˘ÔÏÔÁ›˙Ô˘Ó ÓÔÂÚ¿ Î·È ·ÚÔ˘ÛÈ¿˙Ô˘Ó ÚÔÊÔÚÈο ÙÔÓ ÙÚfiÔ Ì ÙÔÓ ÔÔ›Ô ˘ÔÏfiÁÈÛ·Ó.

3

Ë

ÂÓfiÙËÙ· 6

¶fiÛ· ¯Ú‹Ì·Ù· ›ӷÈ; ™˘Ó‰¤ˆ Ì ̛· ÁÚ·ÌÌ‹ Ù· ›Û· ÔÛ¿.

∂›Ó·È ... ÏÂÙ¿.

∂›Ó·È ... ÏÂÙ¿.

∂›Ó·È ... ÏÂÙ¿.

∂›Ó·È ... ÏÂÙ¿.

∂›Ó·È ... ÏÂÙ¿.

∂›Ó·È ... ÏÂÙ¿.

∂›Ó·È ... ÏÂÙ¿.

∂›Ó·È ... ÏÂÙ¿.

ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

6 + 6 = ...

7 + 6 = ...

5 + 7 = ...

20+ ... = 25

6 + 5 = ...

20+ 6 = ...

8 + 8 = ...

9 + 9 = ...

37 – 7 = ... 8 + 5 = ...

4

5

43 – ... = 40

30 + ... = 38 10 + 10 + 10 + 10 = ... 7 + 7 = ...

10 + 10 + 10 + 9 = ... 31

45

÷ڿÍÂȘ, ·˙Ï Î·È ÌˆÛ·˚ο

1 ªÂÙÚÒ Î·È Áڿʈ ÙÔÓ ·ÚÈıÌfi ÙˆÓ Û¯ËÌ¿ÙˆÓ Ù˘ ·Ú·Î¿Ùˆ ÂÈÎfiÓ·˜.

....... .......

2 ∂ÓÒÓˆ Ì ÙÔ ¯¿Ú·Î· Ù· ÛËÌ›· Ô˘ ¤¯Ô˘Ó ÙÔ ›‰ÈÔ ¯ÚÒÌ·. OÓÔÌ¿˙ˆ Ù· Û¯‹Ì·Ù· Ô˘ ‰ËÌÈÔ˘ÚÁÔ‡ÓÙ·È Ì ·˘ÙfiÓ ÙÔÓ ÙÚfiÔ Î·È Ù· ¯ÚˆÌ·Ù›˙ˆ Ì ÙÔ ·ÓÙ›ÛÙÔÈ¯Ô ¯ÚÒÌ· ÙˆÓ ÛËÌ›ˆÓ.

32

Ë

ÂÓfiÙËÙ· 7 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ·ıÚÔ›ÛÌ·Ù· Ì ÙÚÂȘ ÚÔÛıÂÙ¤Ô˘˜.

3

4 ∂ÓÒÓˆ Ì ÌÈ· ÁÚ·ÌÌ‹ Ù· ÎÔÌÌ¿ÙÈ· Ô˘, ·Ó Û˘Ó‰ÂıÔ‡Ó, Û¯ËÌ·Ù›˙Ô˘Ó ¤Ó· ÙÂÙÚ¿ÁˆÓÔ, ÙÚ›ÁˆÓÔ ‹ ÔÚıÔÁÒÓÈÔ.

3. ¶ÚÔÙ›ÓÔ˘Ì ÚÔÛı¤ÛÂȘ ̤¯ÚÈ ÙÔ 10 Ì ÙÚÂȘ ÚÔÛıÂÙ¤Ô˘˜, ÛÙȘ Ôԛ˜ ÔÈ ‰‡Ô ÚÔÛıÂÙ¤ÔÈ Â›Ó·È fiÌÔÈÔÈ (.¯. 2 + 2 + 3, 3 + 3 + 2 Î.Ï.).

33

46

¶ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ‰È„‹ÊÈˆÓ Î·È ÌÔÓÔ„‹ÊÈˆÓ ·ÚÈıÌÒÓ

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ıÚÔ›ÛÌ·Ù· Î·È ÙȘ ‰È·ÊÔÚ¤˜.

1

2 ∆· ÁÂÓ¤ıÏÈ· Ù˘ MfiÓ· ∏ MfiÓ· ÁÈÔÚÙ¿˙ÂÈ Ù· ÁÂÓ¤ıÏÈ¿ Ù˘. ¶fiÛˆÓ ¯ÚfiÓˆÓ Â›Ó·È; ŒÓ· ÌÂÁ¿ÏÔ ÎÂÚ› ÈÛÔ‰˘Ó·Ì› Ì 10 ÌÈÎÚ¿ ÎÂÚ¿ÎÈ·.

∏ MfiÓ· Â›Ó·È ........ ¯ÚfiÓˆÓ. ¶fiÛˆÓ ¯ÚfiÓˆÓ ı· Â›Ó·È ¤ÂÈÙ· ·fi 3 ¯ÚfiÓÈ·;

¶fiÛˆÓ ¯ÚfiÓˆÓ ‹Ù·Ó ÚÈÓ ·fi 2 ¯ÚfiÓÈ·;

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ.

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ.

....................................................

.................................................

3 YÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ ·ÔÙ¤ÏÂÛÌ·.

14+ 1 = ... 15 + 3 = ... 15 – 3 = ... 18 – 4 = ... 15 + 2 = ... 13 + 3 = ... 14 – 2 = ... 17 – 2 = ... 14 + 4 = ... 12 + 2 = ... 16 – 3 = ... 16 – 4 = ... 34

1. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÚÔÛı¤ÛÂȘ ‰È„‹ÊÈÔ˘ Ì ÌÔÓÔ„‹ÊÈÔ ·ÚÈıÌfi Î·È ·Ê·ÈÚ¤ÛÂȘ ÌÔÓÔ„‹ÊÈÔ˘ ·fi ‰È„‹ÊÈÔ ·ÚÈıÌfi (.¯. 12 + 2, 16 – 3 Î.Ï.).

Ë

ÂÓfiÙËÙ· 7 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ıÚÔ›ÛÌ·Ù· Î·È ÙȘ ‰È·ÊÔÚ¤˜.

4

5 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

2 + ... = 4 12 + ... = 14 6 – ... = 3 16 – ... = 13

5 + ... = 9 15 + ... = 19 8 – ... = 7 18 – ... = 17

2 + ... = 7 12 + ... = 17 9 – ... = 2 19 – ... = 12 6

£¤Ïˆ Ó· ‚¿Ïˆ 9 ÌÈÛÎfiÙ· Û 3 Û·ÎÔ˘Ï¿ÎÈ·. µÚ›ÛΈ Î·È Áڿʈ ÙÚÂȘ ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜.

... + ... + ... = ... ... + ... + ... = ... ... + ... + ... = ... 4. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÚÔÛı¤ÛÂȘ ‰È„‹ÊÈÔ˘ Ì ÌÔÓÔ„‹ÊÈÔ ·ÚÈıÌfi Î·È ·Ê·ÈÚ¤ÛÂȘ ÌÔÓÔ„‹ÊÈÔ˘ ·fi ‰È„‹ÊÈÔ ·ÚÈıÌfi (.¯. 15 + 4, 19 – 3 Î.Ï.). 35

47

H ÚfiÛıÂÛË Î·È Ë ·Ê·›ÚÂÛË ˆ˜ ·ÓÙ›ÛÙÚÔʘ Ú¿ÍÂȘ – ∏ ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜

1 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

14 – 6 =

16 – 7 =

–6

–7

14

16 –4

–2 10

10

13 – 5 =

17 – 9 =

–5

–9

13

17 10

10

12 – 5 =

13 – 7 =

–5 12

13 10

36

–7

10

Ë

ÂÓfiÙËÙ· 7

2

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙȘ ÚÔÛı¤ÛÂȘ.

3 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ ·ÔÙ¤ÏÂÛÌ·.

9 + 8 = ...

7 + 4 = ...

4 + 8 = ...

17 – 8 = ...

11 – 4 = ...

12 – 4 = ...

18 + 4 = ...

17 + 5 = ...

19 + 4 = ...

22 – 4 = ...

22 – 5 = ...

23 – 4 = ... 4

Ãڈ̷ٛ˙ˆ Ù· Ì·ÏfiÓÈ· Ì ÙÔ ¯ÚÒÌ· Ô˘ Ú¤ÂÈ.

6+6 5+6

7+5

4+8

3+9

9+6

7+7

8+6

8+2

14 12 2. ¶ÚÔÙ›ÓÔ˘Ì ·ıÚÔ›ÛÌ·Ù· Ô˘ Â›Ó·È ‰˘Ó·Ùfi Ó· ˘ÔÏÔÁÈÛÙÔ‡Ó Ì ÙË Ì¤ıÔ‰Ô Ù˘ ˘¤Ú‚·Û˘ Ù˘ ‰Âο‰·˜ (.¯. 8 + 5, 9 + 7, 3 + 8 Î.Ï.).

37

48

ÀÔÏÔÁÈÛÌÔ› – ∂ÈÛÙÚÔÊ‹ ÛÙËÓ ÂÓÙ¿‰· ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙȘ ·Ê·ÈÚ¤ÛÂȘ.

1

2 ¶fiÛÔ Î¿ÓÔ˘Ó 8 + 6; ªÂÙÚÒ

ÀÔÏÔÁ›˙ˆ

8 + 6 = ...

8 = 5 + ... 6 = ... + ... 8 + 6 = ...

ÀÔÏÔÁ›˙ˆ Ù· ·Ú·Î¿Ùˆ ·ıÚÔ›ÛÌ·Ù·.

7+6

8+5

7 = ... + ... 6 = ... + ... 7 + 6 = ...

8 = ... + ... 8 + 5 = ... 3

ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ ·ÔÙ¤ÏÂÛÌ·.

38

9 + 5 = ...

9 + 7 = ...

8 – 5 = ...

9 + 6 = ...

10+ 6 = ...

10– 5 = ...

10+ 5 = ...

7 – 5 = ...

9 – 5 = ...

1. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ ÛÙ· ·È‰È¿ ·Ê·ÈÚ¤ÛÂȘ Ù˘ ÌÔÚÊ‹˜ Ó – 5, fiÔ˘ Ó ¤Ó·˜ ·ÚÈıÌfi˜ ·fi ÙÔ 6 ̤¯ÚÈ ÙÔ 10 (.¯. 7 – 5, 8 – 5 Î.Ï.).

Ë

ÂÓfiÙËÙ· 7 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙÔ ¿ıÚÔÈÛÌ·.

4

5 ÀÔÏÔÁ›˙ˆ Ù· ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù·.

6+6

7+7

6 = 5 + ... 6 + 6 = ...

7 = ... + ... 7 + 7 = ...

8+8

9+9

8 = ... + ... 8 + 8 = ...

9 = ... + ... 9 + 9 = ... 6

¶fiÛ· fi‰È· ¤¯Ô˘Ó Ù· ‰‡Ô ¯Ù·fi‰È·;

T· ‰‡Ô ¯Ù·fi‰È· ¤¯Ô˘Ó ... fi‰È·.

¶fiÛ· Â›Ó·È fiÏ· Ù· ¯Ú‹Ì·Ù·;

ŸÏ· Ù· ¯Ú‹Ì·Ù· Â›Ó·È ... ú.

4. ∏ ‰·ÛοϷ ÚÔÙ›ÓÂÈ ·ıÚÔ›ÛÌ·Ù· Ì ÚÔÛıÂÙ¤Ô˘˜ ·fi ÙÔ 5 ̤¯ÚÈ ÙÔ 10 (.¯. 10 + 5, 7 + 5 Î.Ï.). 39

49

¶ÚfiÛıÂÛË Î·È ·Ê·›ÚÂÛË – ¢È„‹ÊÈÔÈ Î·È ÌÔÓÔ„‹ÊÈÔÈ ·ÚÈıÌÔ›

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙÔ ·ÔÙ¤ÏÂÛÌ· ÙˆÓ ·Ê·ÈÚ¤ÛˆÓ.

1

2 ÀÔÏÔÁ›˙ˆ ÙȘ ·Ê·ÈÚ¤ÛÂȘ Ì ÚfiÛıÂÛË ÚÔ˜ Ù· Â¿Óˆ.

12 – 8 = ... 8 + ... = 10 10 + ... = 12

13 – 7 = ...

14 – 9 = ...

15 – 12 = ...

3 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

9 + 6 = ... 10 + ... = 17 8 + 4 = ... 15 – ... = 10

40

13 - 8 = ... 10 + 12 = ... 12 – 7 = ... 8 + 9 = ...

7 + 4 = ... 16 – 7 = ... 23 – 3 = ... 16 – 8 = ...

1. ¶ÚÔÙ›ÓÔ˘Ì ·Ú¯Èο ·Ê·ÈÚ¤ÛÂȘ ÌÔÓÔ„‹ÊÈÔ˘ ·fi ‰È„‹ÊÈÔ ·ÚÈıÌfi Ù˘ ÌÔÚÊ‹˜ 1Ó – Ó, (.¯. 15 – 5, 17 – 7 Î.Ï.). ™ÙË Û˘Ó¤¯ÂÈ· ÚÔÙ›ÓÔ˘Ì ·Ê·ÈÚ¤ÛÂȘ, fiˆ˜ 12 – 4, 17 – 8 Î.Ï., ÔÈ Ôԛ˜ ÂÎÙÂÏÔ‡ÓÙ·È Î·È Ì ÙËÓ ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜.

Ë

ÂÓfiÙËÙ· 7

4

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙÔ ·ÔÙ¤ÏÂÛÌ· ÙˆÓ ·Ê·ÈÚ¤ÛˆÓ.

5 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

+3

+6

9

7 10

8

10

13

11

6

10

10

–6

–7

13

9

15

10

10

8

12 10

7

11

10

4. ¶ÚÔÙ›ÓÔ˘Ì ·Ê·ÈÚ¤ÛÂȘ fiˆ˜ 12 – 6, 15 – 7, 16 – 8 Î.Ï. OÈ Ì·ıËÙ¤˜ ˘ÔÏÔÁ›˙Ô˘Ó ÓÔÂÚ¿ Î·È ÂÍËÁÔ‡Ó ÙÔÓ ÙÚfiÔ ˘ÔÏÔÁÈÛÌÔ‡.

41

50

¶ÚÔ‚Ï‹Ì·Ù· ™ÙËÓ ·˘Ï‹ ÙÔ˘ Û¯ÔÏ›Ԣ

1

™ÙËÓ ·˘Ï‹ ÙÔ˘ Û¯ÔÏ›Ԣ ‚Á‹Î·Ó 5 ÎÔÚ›ÙÛÈ·. ™Â Ï›ÁÔ ‚Á‹Î·Ó Î·È ·ÁfiÚÈ·. ª¤ÙÚËÛ· Ù· ·ÁfiÚÈ· Î·È ‚ڋη fiÙÈ ‹Ù·Ó 3 ·Ú·¿Óˆ ·fi Ù· ÎÔÚ›ÙÛÈ·. ¶fiÛ· ‹Ù·Ó Ù· ·ÁfiÚÈ·;

¶fiÛ· ‹Ù·Ó fiÏ· Ì·˙› Ù· ·È‰È¿;

∆· ·ÁfiÚÈ· ‹Ù·Ó ...

ŸÏ· Ù· ·È‰È¿ Ì·˙› ‹Ù·Ó ...

2 O ¶˘ı·ÁfiÚ·˜ ›¯Â 4 ÁÚ·ÌÌ·ÙfiÛËÌ·. ∏ ª·Ú›Ó· ÙÔ˘ ¤‰ˆÛ ¿ÏÏ· 2. ∏ ∫·ÙÂÚ›Ó· ÙÔ˘ ¤‰ˆÛ 2 ·ÎfiÌË Î·È Ô ∞fiÛÙÔÏÔ˜ ÙÔ˘ ¤‰ˆÛ ÌÂÚÈο ·ÎfiÌË. ∆ÒÚ· Ô ¶˘ı·ÁfiÚ·˜ ¤¯ÂÈ 10 ÁÚ·ÌÌ·ÙfiÛËÌ·. O ∞fiÛÙÔÏÔ˜ ÙÔ˘ ¤‰ˆÛ ... ÁÚ·ÌÌ·ÙfiÛËÌ·. 42

Ë

ÂÓfiÙËÙ· 7

3 ªÔÚ›˜ Ó· ‚ÚÂȘ ¤Ó·Ó ÙÚfiÔ ÁÈ· Ó· ¤¯ÂȘ 12 ÏÂÙ¿ Ì ٤ÛÛÂÚ· ÓÔÌ›ÛÌ·Ù·; ∑ˆÁÚ¿ÊÈÛ ٷ ÓÔÌ›ÛÌ·Ù·.

4 ■ ™ÙÔ Ì¿ıËÌ· Ù˘ Á˘ÌÓ·ÛÙÈ΋˜ 8 ·È‰È¿ ·›˙Ô˘Ó Ô‰fiÛÊ·ÈÚÔ, ÂÓÒ Ù· ˘fiÏÔÈ· 6 ·›˙Ô˘Ó Î·Ï·ıÔÛÊ·›ÚÈÛË. ¶fiÛ· Â›Ó·È fiÏ· Ù· ·È‰È¿ ÛÙÔ Ì¿ıËÌ· Ù˘ Á˘ÌÓ·ÛÙÈ΋˜;

A¿ÓÙËÛË

¢È·Ù˘ÒÓˆ ¤Ó· ‰ÈÎfi ÌÔ˘ Úfi‚ÏËÌ· ■ ™Î¤„Ô˘ ¤Ó· ·ÚfiÌÔÈÔ Ì ÙÔ ÚÔËÁÔ‡ÌÂÓÔ Úfi‚ÏËÌ·, ¯ÚËÛÈÌÔÔÈÒÓÙ·˜ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ 9 Î·È 7.

¢ÒÛ ÙÔ Úfi‚ÏËÌ· Ó· ÙÔ Ï‡ÛÂÈ Ô ‰ÈÏ·Ófi˜ ÛÔ˘. 43

51

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ·

1

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙȘ Ú¿ÍÂȘ.

2 ™˘ÁÎÚ›Óˆ ÙÔ˘˜ ‚fiÏÔ˘˜.

°ÈÒÚÁÔ˜

N›ÎÔ˜

O °ÈÒÚÁÔ˜ ¤¯ÂÈ 12 ‚fiÏÔ˘˜ Î·È Ô ¡›ÎÔ˜ 8 ‚fiÏÔ˘˜. ¶fiÛÔ˘˜ ÂÚÈÛÛfiÙÂÚÔ˘˜ ‚fiÏÔ˘˜ ¤¯ÂÈ Ô °ÈÒÚÁÔ˜; ªÂ ÙÔÓ ›‰ÈÔ ÙÚfiÔ ˘ÔÏfiÁÈÛ ÙȘ ·Ú·Î¿Ùˆ Ú¿ÍÂȘ:

12 ‚fiÏÔ˘˜

8 ‚fiÏÔ˘˜

13 – 7 = ...

11 – 9 = ...

13 – 8 = ...

11 – 7 = ... 3

ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

3 + ... = 5 13 + ... = 15 4 + ... = 8 14 + ... = 18 5 + ... = 9 15 + ... = 19 44

4 + ... = 7 14 + ... = 17 6 – ... = 3 16 – ... = 13 8 – ... = 6 18 – ... = 16

9 – ... = 7 19 – ... = 17 8 – ... = 2 18 – ... = 12 7 – ... = 6 17 – ... = 16

1. ¶ÚÔÙ›ÓÔ˘Ì ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ÔÈ Ôԛ˜ ÚÔÛʤÚÔÓÙ·È ÁÈ· Â›Ï˘ÛË Ì ÙËÓ ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜, Ì ٷ ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù· ‹ Ì ¿ÏÏÔ˘˜ ÙÚfiÔ˘˜ (.¯. 7 + 8, 2 + 9, 18 – 9, 13 – 5 Î.Ï.).

Ë

ÂÓfiÙËÙ· 7

4

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙȘ Ú¿ÍÂȘ.

5 Ãڈ̷ٛ˙ˆ ÙȘ Ì¿Ï˜ Ì ÙÔ ·ÓÙ›ÛÙÔÈ¯Ô ¯ÚÒÌ·.

11 8 7 9 4 + 7 = ...

14 – 6 = ...

13 – 4 = ...

13 – 6 = ... 17 – 8 = ... 2 + 9 = ... 15 – 7 = ...

15– 8 = ...

4. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÚÔÛı¤ÛÂȘ ‰È„‹ÊÈÔ˘ Ì ÌÔÓÔ„‹ÊÈÔ ·ÚÈıÌfi Î·È ·Ê·ÈÚ¤ÛÂȘ ÌÔÓÔ„‹ÊÈÔ˘ ·fi ‰È„‹ÊÈÔ ·ÚÈıÌfi (.¯. 12 + 2, 16 – 3 Î.Ï.). 45

ªÂ ·fiÊ·ÛË Ù˘ ∂ÏÏËÓÈ΋˜ ∫˘‚¤ÚÓËÛ˘ Ù· ‰È‰·ÎÙÈο ‚È‚Ï›· ÙÔ˘ ¢ËÌÔÙÈÎÔ‡, ÙÔ˘ °˘ÌÓ·Û›Ô˘ Î·È ÙÔ˘ §˘Î›Ԣ Ù˘ÒÓÔÓÙ·È ·fi ÙÔÓ √ÚÁ·ÓÈÛÌfi ∂ΉfiÛˆ˜ ¢È‰·ÎÙÈÎÒÓ µÈ‚Ï›ˆÓ Î·È ‰È·Ó¤ÌÔÓÙ·È ‰ˆÚÂ¿Ó ÛÙ· ¢ËÌfiÛÈ· ™¯ÔÏ›·. ∆· ‚È‚Ï›· ÌÔÚ› Ó· ‰È·Ù›ıÂÓÙ·È ÚÔ˜ ÒÏËÛË, fiÙ·Ó Ê¤ÚÔ˘Ó ‚È‚ÏÈfiÛËÌÔ ÚÔ˜ ·fi‰ÂÈÍË Ù˘ ÁÓËÛÈfiÙËÙ¿˜ ÙÔ˘˜. ∫¿ı ·ÓÙ›Ù˘Ô Ô˘ ‰È·Ù›ıÂÙ·È ÚÔ˜ ÒÏËÛË Î·È ‰Â ʤÚÂÈ ‚È‚ÏÈfiÛËÌÔ, ıˆÚÂ›Ù·È ÎÏ„›Ù˘Ô Î·È Ô ·Ú·‚¿Ù˘ ‰ÈÒÎÂÙ·È Û‡Ìʈӷ Ì ÙȘ ‰È·Ù¿ÍÂȘ ÙÔ˘ ¿ÚıÚÔ˘ 7, ÙÔ˘ ¡fiÌÔ˘ 1129 Ù˘ 15/21 ª·ÚÙ›Ô˘ 1946 (ºEK 1946, 108, Aã).

BIB§IO™HMO

∞·ÁÔÚ‡ÂÙ·È Ë ·Ó··Ú·ÁˆÁ‹ ÔÔÈÔ˘‰‹ÔÙ ÙÌ‹Ì·ÙÔ˜ ·˘ÙÔ‡ ÙÔ˘ ‚È‚Ï›Ô˘, Ô˘ ηχÙÂÙ·È ·fi ‰ÈηÈÒÌ·Ù· (copyright), ‹ Ë ¯Ú‹ÛË ÙÔ˘ Û ÔÔÈ·‰‹ÔÙ ÌÔÚÊ‹, ¯ˆÚ›˜ ÙË ÁÚ·Ù‹ ¿‰ÂÈ· ÙÔ˘ ¶·È‰·ÁˆÁÈÎÔ‡ πÓÛÙÈÙÔ‡ÙÔ˘.

52

OÈ ·ÚÈıÌÔ› ̤¯ÚÈ ÙÔ 70

1 ¶ÔÈÔÈ ·ÚÈıÌÔ› ›ӷÈ;

= ¢Âο‰Â˜

= MÔÓ¿‰Â˜

ªÂÙÚÒ Î·È Áڿʈ ÙȘ ‰Âο‰Â˜ Î·È ÙȘ ÌÔÓ¿‰Â˜.

¢ M

¢ M

™¯ËÌ·Ù›˙ˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ ÛÙÔ˘˜ ¿‚·Î˜.

°Ú¿Êˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜.

10

¢ M

Ë

ÂÓfiÙËÙ· 8 YÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙȘ Ú¿ÍÂȘ.

ΔÔ ÍÂÓԉԯ›Ô

2

3

6Ô˜ fiÚÔÊÔ˜ 4Ô˜ fiÚÔÊÔ˜ 3Ô˜ fiÚÔÊÔ˜ 1Ô˜ fiÚÔÊÔ˜ IÛfiÁÂÈÔ ™Â οı fiÚÔÊÔ ˘¿Ú¯Ô˘Ó 10 ‰ˆÌ¿ÙÈ·. O ¶ÂÚÈÎÏ‹˜ ̤ÓÂÈ ÛÙÔ ‰ˆÌ¿ÙÈÔ 54. ™Â ÔÈÔÓ fiÚÔÊÔ Â›Ó·È; ∂›Ó·È ÛÙÔÓ ... fiÚÔÊÔ. ∏ ¡·Ù·Ï›· ̤ÓÂÈ ÛÙÔ ‰ˆÌ¿ÙÈÔ 48 Î·È Ô °È¿ÓÓ˘ ÛÙÔ ‰ˆÌ¿ÙÈÔ 70. ª¤ÓÔ˘Ó ÛÙÔÓ ›‰ÈÔ fiÚÔÊÔ; ¡∞π

OÃπ

2. ¶ÚÔÙ›ÓÔ˘Ì ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ‰È„‹ÊÈˆÓ ·ÚÈıÌÒÓ Ì Ï‹ÚÂȘ ‰Âο‰Â˜ ̤¯ÚÈ ÙÔ 70 (.¯. 30 + 40, 70 – 20 Î.Ï.). ¶ÚÔÙ›ÓÔ˘Ì Â›Û˘ ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ‰È„‹ÊÈˆÓ ·ÚÈıÌÒÓ Î·Ù¿ ÙȘ Ôԛ˜ Ô ‰Â‡ÙÂÚÔ˜ ·ÚÈıÌfi˜ Â›Ó·È ‰È„‹ÊÈÔ˜ Ì Ï‹ÚÂȘ ‰Âο‰Â˜ (.¯. 34 + 20, 66 – 30 Î.Ï.).

11

53

∂ÈÛ·ÁˆÁ‹ ÛÙÔÓ ÔÏÏ·Ï·ÛÈ·ÛÌfi

1

ªÂÙÚÒ ·Ó¿ 2 ̤¯ÚÈ ÙÔ 20.

2

4

6

...

20 2

Δ· ·È‰È¿, ÚÈÓ Ó· ÌÔ˘Ó ÛÙÔ ‰ˆÌ¿ÙÈÔ, ¤‚Á·Ï·Ó Ù· ·Ô‡ÙÛÈ· ÙÔ˘˜. ¶fiÛ· ·È‰È¿ Â›Ó·È Ì¤Û· ÛÙÔ ‰ˆÌ¿ÙÈÔ;

E›Ó·È

·È‰È¿.

3 ∫¿ı ·ÛÙÂÚ›·˜ ¤¯ÂÈ 5 fi‰È·. ¶fiÛ· fi‰È· ¤¯Ô˘Ó ÔÈ 3 ·ÛÙÂڛ˜; ÊÔÚ¤˜ ÙÔ

=

OÈ 3 ·ÛÙÂڛ˜ ¤¯Ô˘Ó

fi‰È·.

¶fiÛ· fi‰È· ¤¯Ô˘Ó ÔÈ 5 ·ÛÙÂڛ˜; ÊÔÚ¤˜ ÙÔ

OÈ 5 ·ÛÙÂڛ˜ ¤¯Ô˘Ó

12

=

fi‰È·.

1. OÈ Ì·ıËÙ¤˜ ÌÂÙÚÔ‡Ó ·Ó¿ 2 ̤¯ÚÈ ÙÔ 20. ZËÙԇ̠·fi ÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ÍÂÎÈÓÔ‡Ó Î·È ·fi ·ÚÈıÌÔ‡˜ ‰È·ÊÔÚÂÙÈÎÔ‡˜ ·fi ÙÔ Ìˉ¤Ó (.¯. ·fi ÙÔ 6, ÙÔ 12 Î.Ï.).

Ë

ÂÓfiÙËÙ· 8

4 ∏ B¿Ûˆ ·ÁfiÚ·Û 4 ·Î¤Ù· Ì ̷ÛÙ›¯Â˜. ∫¿ı ·Î¤ÙÔ Â›¯Â ̤۷ 5 Ì·ÛÙ›¯Â˜. ¶fiÛ˜ Â›Ó·È fiϘ ÔÈ Ì·ÛÙ›¯Â˜ Ô˘ ·ÁfiÚ·ÛÂ Ë μ¿Ûˆ;

ÊÔÚ¤˜ ÙÔ

=

ŸÏ˜ ÔÈ Ì·ÛÙ›¯Â˜ Â›Ó·È ¶fiÛ· fi‰È· ¤¯Ô˘Ó 4 Û΢ÏÈ¿; ÊÔÚ¤˜ ÙÔ

T· 4 Û΢ÏÈ¿ ¤¯Ô˘Ó

=

fi‰È·.

5 ªÔÈÚ¿˙ˆ ÂÍ›ÛÔ˘ Ù· 12 ·‚Á¿ ÛÙȘ 3 ʈÏȤ˜. ∑ˆÁÚ·Ê›˙ˆ Ù· ·‚Á¿ ÛÙȘ ʈÏȤ˜.

Y¿Ú¯Ô˘Ó

3 ÊÔÚ¤˜ ÙÔ

·‚Á¿ Û οı ʈÏÈ¿.

= 13

54

ª¤ÙÚËÛË ÌÂÁÂıÒÓ

1 ¶fiÛ· ÙÂÙÚ·ÁˆÓ¿ÎÈ· Â›Ó·È ÙÔ Ì‹ÎÔ˜ οı ÌÔÏ˘‚ÈÔ‡; ™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÓÙ›ÛÙÔÈ¯Ô˘˜ ·ÚÈıÌÔ‡˜.

10

2 ΔÚ·‚Ò ÌÈ· ÁÚ·ÌÌ‹ ÈÔ Ì·ÎÚÈ¿ ·fi ·˘Ù‹ Ô˘ ‚Ϥˆ Ì ÎfiÎÎÈÓÔ ¯ÚÒÌ· Î·È ÌÈ· ÈÔ ÎÔÓÙ‹ Ì Ú¿ÛÈÓÔ ¯ÚÒÌ·.

3 Ãڈ̷ٛ˙ˆ Ì ÙÔ ›‰ÈÔ ¯ÚÒÌ· ÙȘ Ú¿‚‰Ô˘˜ Ô˘ ¤¯Ô˘Ó ›‰ÈÔ Ì‹ÎÔ˜.

14

Ë

ÂÓfiÙËÙ· 8

4 ªÈ· ηӿٷ ÁÂÌ›˙ÂÈ ‰‡Ô ÔÙ‹ÚÈ·. Ãڈ̷ٛ˙ˆ Ù· ÔÙ‹ÚÈ· Ô˘ ÁÂÌ›˙Ô˘Ó Î¿ı ÊÔÚ¿ ÔÈ Î·Ó¿Ù˜.

5 ¶·Ú·ÙËÚÒ Ù· ¯ÚˆÌ·ÙÈṲ̂ӷ Û¯‹Ì·Ù·. Ãڈ̷ٛ˙ˆ Ì ÙÔ ·ÓÙ›ÛÙÔÈ¯Ô ¯ÚÒÌ· Ù· ›‰È· Û¯‹Ì·Ù·.

15

55

¶ÚfiÛıÂÛË Î·È ·Ê·›ÚÂÛË ‰È„‹ÊÈˆÓ ·ÚÈıÌÒÓ ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ÔÙÂϤÛÌ·Ù· ÙˆÓ ڿ͈Ó.

1

2 ¶fiÛ· ÏÂÙ¿ ˘¿Ú¯Ô˘Ó ÛÙÔ ÎfiÎÎÈÓÔ ÔÚÙÔÊfiÏÈ;

20 + ....................................

¶fiÛ· ÏÂÙ¿ ˘¿Ú¯Ô˘Ó ÛÙÔ Ú¿ÛÈÓÔ ÔÚÙÔÊfiÏÈ; ..................................... ¶fiÛ· ÏÂÙ¿ ˘¿Ú¯Ô˘Ó Î·È ÛÙ· ‰‡Ô ÔÚÙÔÊfiÏÈ· Ì·˙›; ......................................

3

20 ÏÂÙ¿

Δ· ¯Ú‹Ì·Ù· Ô˘ ›¯Â Ì·˙› ÙÔ˘ Ô ∞fiÛÙÔÏÔ˜ ‹Ù·Ó ‰‡Ô ÓÔÌ›ÛÌ·Ù· ÙˆÓ 20 ÏÂÙÒÓ Î·È ¤Ó· ÙˆÓ 10 ÏÂÙÒÓ. ∞ÁfiÚ·Û ·fi ÙÔ ÂÚ›ÙÂÚÔ Î·Ú·Ì¤Ï˜ Î·È Ï‹ÚˆÛ 20 ÏÂÙ¿. ¶fiÛ· ÏÂÙ¿ ÙÔ˘ ¤ÌÂÈÓ·Ó; O ∞fiÛÙÔÏÔ˜ ›¯Â ... ÏÂÙ¿. ΔÔ˘ ¤ÌÂÈÓ·Ó... ÏÂÙ¿.

16

1. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ Ì ‰Âο‰Â˜ (.¯. 60 + 30, 50 – 40 Î.Ï.).

Ë

ÂÓfiÙËÙ· 8

4

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ÔÙÂϤÛÌ·Ù· ÙˆÓ ڿ͈Ó.

23 + 3 65 –40

5

ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙÔ ·ÔÙ¤ÏÂÛÌ· ÙˆÓ ڿ͈Ó.

34 +20

25 +40

59 – 3

50 –20

32 + 7

50 +20

40 +30

67 – 6

60 –30

70 –50

™˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

6

+2

7 9 11

+3

5 8 11 14 4. ¶ÚÔÙ›ÓÔ˘Ì ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ÔÈ Ôԛ˜ ÂÎÙÂÏÔ‡ÓÙ·È Î·È Ì ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜.

17

56

EÈÛ·ÁˆÁ‹ ÛÙË Û˘ÌÌÂÙÚ›·

1 º·ÓÙ¿˙ÔÌ·È ÙÔÓ ÙÚfiÔ Ì ÙÔÓ ÔÔ›Ô ‰ÈÏÒÓÔÓÙ·È ÔÈ ÂÈÎfiÓ˜ Î·È ‰È·Áڿʈ ÂΛӘ ÛÙȘ Ôԛ˜ ‰ÂÓ Û˘Ì›ÙÔ˘Ó Ù· ‰‡Ô ̤ÚË.

2 ™˘ÌÏËÚÒÓˆ Ù· Û¯‹Ì·Ù·, ÒÛÙ ӷ Á›ÓÔ˘Ó Û˘ÌÌÂÙÚÈο ˆ˜ ÚÔ˜ ÙËÓ ÎfiÎÎÈÓË ÁÚ·ÌÌ‹. º·ÓÙ¿˙ÔÌ·È ÙÔÓ ÙÚfiÔ Ì ÙÔÓ ÔÔ›Ô ‰ÈÏÒÓÔÓÙ·È ÔÈ ÂÈÎfiÓ˜.

18

Ë

ÂÓfiÙËÙ· 8 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ÔÙÂϤÛÌ·Ù· ÙˆÓ ڿ͈Ó.

3

4 ÷ڿ˙ˆ Ì ÙÔ ¯¤ÚÈ ÁÈ· Ó· Û˘ÌÏËÚÒÛˆ Ù· ÁÚ¿ÌÌ·Ù·. Δ· ÁÚ¿ÌÌ·Ù· Â›Ó·È Û˘ÌÌÂÙÚÈο ˆ˜ ÚÔ˜ ÙËÓ ÎfiÎÎÈÓË ÁÚ·ÌÌ‹.

5 μ¿˙ˆ Û ·ÎÏÔ Ù· 5 Ï¿ıË Ô˘ ˘¿Ú¯Ô˘Ó ÛÙËÓ ·Ú·Î¿Ùˆ ÂÈÎfiÓ·.

3. ¶ÚÔÙ›ÓÔ˘Ì ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ÔÈ Ôԛ˜ ÚÔÛʤÚÔÓÙ·È ÁÈ· Â›Ï˘ÛË Ì ÙËÓ ˘¤Ú‚·ÛË Ù˘ ‰Âο‰·˜, Ù· ‰ÈÏ¿ ·ıÚÔ›ÛÌ·Ù· ‹ Ì ¿ÏÏÔ˘˜ ÙÚfiÔ˘˜ (.¯. 7 + 8, 18 – 9, 13 – 5 Î.Ï.).

19

57

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ· ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ÔÙÂϤÛÌ·Ù· ÙˆÓ ڿ͈Ó.

1

2 μ¿˙ˆ Û ·ÎÏÔ Ù· ÓÔÌ›ÛÌ·Ù· Ô˘ Ú¤ÂÈ.

47 ÏÂÙ¿

69 ÏÂÙ¿

3 ™˘ÌÏËÚÒÓˆ ÙÔ ·ÔÙ¤ÏÂÛÌ· Î·È Áڿʈ ÙÔ ¿ıÚÔÈÛÌ·.

20

4 ÊÔÚ¤˜ ÙÔ 2 =

2+2+2+2 ......................................................

3 ÊÔÚ¤˜ ÙÔ 5 =

......................................................

5 ÊÔÚ¤˜ ÙÔ 5 =

......................................................

4 ÊÔÚ¤˜ ÙÔ 10 =

......................................................

6 ÊÔÚ¤˜ ÙÔ 10 =

......................................................

1. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ Ó· οÓÔ˘Ó ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ‰È„‹ÊÈˆÓ ·ÚÈıÌÒÓ Ì Ï‹ÚÂȘ ‰Âο‰Â˜ ̤¯ÚÈ ÙÔ 70 (.¯. 30 + 40, 70 – 20 Î.Ï.). ∂›Û˘ ÚÔÙ›ÓÔ˘Ì ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ‰È„‹ÊÈˆÓ ·ÚÈıÌÒÓ Î·Ù¿ ÙȘ Ôԛ˜ Ô ‰Â‡ÙÂÚÔ˜ ·ÚÈıÌfi˜ Â›Ó·È ‰È„‹ÊÈÔ˜ Ì Ï‹ÚÂȘ ‰Âο‰Â˜ (.¯. 34 + 20, 56 – 30 Î.Ï.).

Ë

ÂÓfiÙËÙ· 8 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ÔÙÂϤÛÌ·Ù· ÙˆÓ ڿ͈Ó.

4

5 ¶·Ú·ÙËÚÒ ÙȘ ÂÈÎfiÓ˜ Î·È ‚¿˙ˆ Û ·ÎÏÔ ÙȘ Û˘ÌÌÂÙÚÈΤ˜.

6 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Ï›Ô˘Ó.

34 +20

39 –10

40 + ... = 70 30 + ... = 60 70 – ... = 50

30 +40

27 +30

60 –40

26 + ... = 56 20 + ... = 45 68 – 20 = ...

4. ¶ÚÔÙ›ÓÔ˘Ì ‰È¿ÊÔÚ· ÁÈÓfiÌÂÓ· ·fi ·˘Ù¿ Ô˘ ¤¯Ô˘Ó ‰È‰·¯ı›. ÃÚËÛÈÌÔÔÈԇ̠ÙË Ï¤ÍË «ÊÔÚ¤˜» (.¯. «2 ÊÔÚ¤˜ ÙÔ 3» Î.Ï.).

21

58

OÈ ·ÚÈıÌÔ› ̤¯ÚÈ ÙÔ 100 – ÃÚ‹Ì·Ù·

1

μÚ›ÛΈ ÙÔÓ ·ÚÈıÌfi Ô˘ ‚Ú›ÛÎÂÙ·È ÚÈÓ Î·È ÌÂÙ¿.

85

86

87 2

μÚ›ÛΈ Î·È Áڿʈ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ Û¯ËÌ·Ù›˙ÔÓÙ·È ÛÙÔ˘˜ ¿‚·Î˜.

3 ™¯ËÌ·Ù›˙ˆ ÛÙÔ˘˜ ¿‚·Î˜ ÙÔ˘˜ ·ÚÈıÌÔ‡˜ Ô˘ ‰›ÓÔÓÙ·È.

87 22

90

76

1. ∏ ‰·ÛοϷ ϤÂÈ ¤Ó·Ó ·ÚÈıÌfi ·fi ÙÔ 70 ̤¯ÚÈ ÙÔ 100 Î·È ÔÈ Ì·ıËÙ¤˜ ηÏÔ‡ÓÙ·È Ó· ‚Ú›ÛÎÔ˘Ó Î¿ı ÊÔÚ¿ ÙÔÓ ÚÔËÁÔ‡ÌÂÓÔ Î·È ÙÔÓ ÂfiÌÂÓÔ ·ÚÈıÌfi.

Ë

ÂÓfiÙËÙ· 9 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ÔÙÂϤÛÌ·Ù· ÙˆÓ ڿ͈Ó.

4

5 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ fiÛ· ∂Àƒø Â›Ó·È Û οı Ï·›ÛÈÔ.

20 + 10 = 30

.....................

.....................

.....................

.....................

.....................

6 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙÔ ·ÔÙ¤ÏÂÛÌ·.

20 + 10 = ... 50 + 10 = ...

50 + 20 = ... 30 + 20 = ...

50 + 50 = ... 40 + 40 = ...

20 + 20 = ...

30 + 30 = ...

50 + 30 = ...

4. ¶ÚÔÙ›ÓÔ˘Ì ÚÔÛı¤ÛÂȘ ‰È„‹ÊÈÔ˘ Ì ÌÔÓÔ„‹ÊÈÔ ·ÚÈıÌfi Î·È ·Ê·ÈÚ¤ÛÂȘ ÌÔÓÔ„‹ÊÈÔ˘ ·fi ‰È„‹ÊÈÔ ·ÚÈıÌfi. OÈ ‰È„‹ÊÈÔÈ ·ÚÈıÌÔ› Ú¤ÂÈ Ó· Â›Ó·È ·fi ÙÔ 50 ̤¯ÚÈ ÙÔ 100 (.¯. 65 + 3, 78 – 4 Î.Ï.).

23

59

¶ÔÏÏ·Ï·ÛÈ·ÛÌfi˜ Î·È ‰È·›ÚÂÛË ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ ÙÔ ·ÔÙ¤ÏÂÛÌ·.

1

2 O ª›ÏÙÔ˜ Â›Ó·È ¿ÚÚˆÛÙÔ˜. ¶‹Á ÛÙÔÓ ·È‰›·ÙÚÔ. ∂ΛÓÔ˜, ·ÊÔ‡ ÙÔÓ ÂͤٷÛÂ, ÙÔ˘ ¤‰ˆÛ ·˘Ù‹Ó ÙË Û˘ÓÙ·Á‹: ¶¤ÙÚÔ˜ I·ÙÚfiÔ˘ÏÔ˜ ¶·È‰›·ÙÚÔ˜ K·ÏÔ‡ 11 TËÏ.: 444-555

3 ¯¿È· ÙËÓ Ë̤ڷ ÁÈ· 4 Ë̤Ú˜

¶fiÛ· ¯¿È· ı· ¿ÚÂÈ Û˘ÓÔÏÈο Ô ª›ÏÙÔ˜;

A¿ÓÙËÛË:

......................................... 3

Δ· ÙÚ›· ·È‰È¿ ı¤ÏÔ˘Ó Ó· ÌÔÈÚ·ÛÙÔ‡Ó ÂÍ›ÛÔ˘ ÙȘ 12 ηڷ̤Ϙ. ¶fiÛ˜ ηڷ̤Ϙ ı· ¿ÚÂÈ Î¿ı ·È‰›;

A¿ÓÙËÛË: ∫¿ı ·È‰› ı· ¿ÚÂÈ ... ηڷ̤Ϙ. 3 ÊÔÚ¤˜ ÙÔ ... = ... 24

1. ¶ÚÔÙ›ÓÔ˘Ì ‰È¿ÊÔÚ· ÁÈÓfiÌÂÓ· ÙÔ˘ 2, ÙÔ˘ 5 Î·È ÙÔ˘ 10. ÃÚËÛÈÌÔÔÈԇ̠ÙË Ï¤ÍË «ÊÔÚ¤˜» (.¯. «2 ÊÔÚ¤˜ ÙÔ 3» Î.Ï.).

Ë

ÂÓfiÙËÙ· 9

4 Δ· ·È‰È¿ ·›˙Ô˘Ó ÛÙËÓ ·˘Ï‹ ÙÔ˘ Û¯ÔÏ›Ԣ. ÈڛÛÙËÎ·Ó Û 4 ÔÌ¿‰Â˜. ∫¿ı ÔÌ¿‰· ·ÔÙÂÏÂ›Ù·È ·fi 5 ·›ÎÙ˜. μ¿˙ˆ Û ·ÎÏÔ ÙË ÛˆÛÙ‹ ÂÈÎfiÓ·.

¶fiÛ· Â›Ó·È fiÏ· Ù· ·È‰È¿ Ô˘ ·›˙Ô˘Ó ÛÙÔ ·È¯Ó›‰È;

A¿ÓÙËÛË:

.................................... ■ ∏ À·Ù›· ¤¯ÂÈ 6 ÓÔÌ›ÛÌ·Ù· ÙˆÓ 5 ÏÂÙÒÓ. ¶fiÛ· ¯Ú‹Ì·Ù· ¤¯ÂÈ;

5

A¿ÓÙËÛË: Œ¯ÂÈ ... ÏÂÙ¿.

■ ∏ À·Ù›· ı¤ÏÂÈ Ó· ·ÓÙ·ÏÏ¿ÍÂÈ Ù· ¯Ú‹Ì·Ù¿ Ù˘ Ì ÓÔÌ›ÛÌ·Ù· ÙˆÓ 10 ÏÂÙÒÓ. ¶fiÛ· ÓÔÌ›ÛÌ·Ù· ÙˆÓ 10 ÏÂÙÒÓ ı· ¿ÚÂÈ;

A¿ÓÙËÛË: £· ¿ÚÂÈ ... ÓÔÌ›ÛÌ·Ù· ÙˆÓ 10 ÏÂÙÒÓ. 25

60

μ¿ÚÔ˜ – §ÂÈÙÔ˘ÚÁ›· ˙˘Á·ÚÈ¿˜

1

ªÂÙÚÒ ·Ó¿ 3 ̤¯ÚÈ ÙÔ 30 Î·È ·Ó¿ 4 ̤¯ÚÈ ÙÔ 40.

3

6

...

30 2

μ¿˙ˆ Û ·ÎÏÔ ÙÔ ‚·Ú‡ÙÂÚÔ.

Ì¿Ï·

·Ô‡ÙÛÈ·

Ì‹ÏÔ

·¯Ï¿‰È

Û·ÏÔ˜

Ï·Áfi˜

°ÈÒÚÁÔ˜ EϤÓË

°ÈÒÚÁÔ˜

EϤÓË

3 ∏ Ì›· ηӿٷ Î·È ÙÔ ¤Ó· ÔÙ‹ÚÈ ¤¯Ô˘Ó ̤۷ ÓÂÚfi, ÂÓÒ Ù· ¿ÏÏ· Â›Ó·È ¿‰ÂÈ·. μ¿˙ˆ Û ·ÎÏÔ ·˘Ù¿ Ô˘ Â›Ó·È ¿‰ÂÈ·.

26

1. ∑ËÙԇ̠·fi ÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ÌÂÙÚ‹ÛÔ˘Ó ÚÔÊÔÚÈο ·Ó¿ 3 ̤¯ÚÈ ÙÔ 30 Î·È ·Ó¿ 4 ̤¯ÚÈ ÙÔ 40.

Ë

ÂÓfiÙËÙ· 9

4 μ¿˙ˆ Û ÛÂÈÚ¿ Ù· ·È‰È¿ ÍÂÎÈÓÒÓÙ·˜ ·fi ÙÔ ÈÔ ‚·Ú‡ Î·È ÊÙ¿ÓÔÓÙ·˜ ÛÙÔ ÈÔ ÂÏ·ÊÚfi. N›ÎÔ˜

AϤη

N›ÎÔ˜

¶¤ÙÚÔ˜

................................... ................................... √ ·ÓÂÏ΢ÛÙ‹Ú·˜

5

∏ ΢ڛ· M·Ú›· ˙˘Á›˙ÂÈ 73 ÎÈÏ¿. O ·ÚÈÔ˜ £ÂfiÊÈÏÔ˜ ˙˘Á›˙ÂÈ 84 ÎÈÏ¿. ¶ÔÈÔ˜ ÌÔÚ› Ó· ¯ÚËÛÈÌÔÔÈ‹ÛÂÈ ÙÔÓ ·ÓÂÏ΢ÛÙ‹Ú·; ¶Ú Ÿ¯È  ÔÛÔ¯‹! ÚÈÛ ·fi 7 ÛfiÙÂÚ· 5 ÎÈÏ¿ !

27

61

÷ڿÍÂȘ Û¯ËÌ¿ÙˆÓ – ¶·˙Ï – ¶Ï·ÎfiÛÙÚˆÙÔ

1 ÷ڿ˙ˆ Ì ÙÔ ¯¿Ú·Î· ÙÔ ›‰ÈÔ Û¯‹Ì· Î·È ÙÔ ¯ÚˆÌ·Ù›˙ˆ Ì ٷ ›‰È· ¯ÚÒÌ·Ù·.

2 μÚ›ÛΈ Î·È Áڿʈ ÙÔ fiÓÔÌ· Î·È ÙÔÓ ·ÚÈıÌfi ÙˆÓ Û¯ËÌ¿ÙˆÓ Ô˘ Â›Ó·È ›‰È·.

28

Ë

ÂÓfiÙËÙ· 9

3 Ãڈ̷ٛ˙ˆ Ù· ÎÔÌÌ¿ÙÈ· Ù˘ ¿È·˜ Ì ٷ ›‰È· ¯ÚÒÌ·Ù·.

4 ™¯Â‰È¿˙ˆ ‰›Ï· Ì ÙÔ ¯¿Ú·Î· Ù· ›‰È· Û¯‹Ì·Ù·.

29

62

¶ÚÔ‚Ï‹Ì·Ù·

1

2ú

O Δ¿ÛÔ˜ ¤¯ÂÈ:

1ú

∏ ·‰ÂÏÊ‹ ÙÔ˘, Ë ª·Ú›·, ¤¯ÂÈ:

■ ¶fiÛ· ·ÚÎÔ˘‰¿ÎÈ· ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ Ô Δ¿ÛÔ˜; O Δ¿ÛÔ˜ ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ .............. ·ÚÎÔ˘‰¿ÎÈ·.

■ ¶fiÛ˜ Ì¿Ï˜ ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ Ô Δ¿ÛÔ˜; O Δ¿ÛÔ˜ ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ ............ Ì¿Ï˜.

■ ¶fiÛ· ·ÚÎÔ˘‰¿ÎÈ· ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ Ë ª·Ú›·; ∏ ª·Ú›· ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ ............ ·ÚÎÔ˘‰¿ÎÈ·.

■ ¶fiÛ˜ Ì¿Ï˜ ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ Ë ª·Ú›·; ∏ ª·Ú›· ÌÔÚ› Ó· ·ÁÔÚ¿ÛÂÈ ........... Ì¿Ï˜. 30

Ë

ÂÓfiÙËÙ· 9

2 O ·ÚÈÔ˜ ¶¤ÙÚÔ˜ ·ÁfiÚ·Û 20 Ì·ÏfiÓÈ·. ™Â οı ·È‰› ı· ‰ÒÛÂÈ ·fi 2 Ì·ÏfiÓÈ·. ¶fiÛ· Ì·ÏfiÓÈ· ı· ÙÔ˘ Ì›ÓÔ˘Ó;

A¿ÓÙËÛË:

.................................... 3

¢È·Ù˘ÒÓˆ ¤Ó· ‰ÈÎfi ÌÔ˘ Úfi‚ÏËÌ· Ì ÚfiÛıÂÛË ‹ ·Ê·›ÚÂÛË. ∫·ÙfiÈÓ ÙÔ ‰›Óˆ ÛÙÔ ‰ÈÏ·Ófi ÌÔ˘ Ó· ÙÔ Ï‡ÛÂÈ.

........................................ ........................................ ........................................ ........................................ ........................................ ........................................ 31

63

E·Ó·ÏËÙÈÎfi Ì¿ıËÌ·

1

ªÂÙÚÒ ·Ó¿ 3 ̤¯ÚÈ ÙÔ 30 Î·È ·Ó¿ 4 ̤¯ÚÈ ÙÔ 40.

3

6

...

30 2

T¤ÛÛÂÚȘ Ó¿ÓÔÈ ·fi ÙÔ ÔχˆÚÔ ÂÚ¿ÙËÌ· ÛÙÔ ‰¿ÛÔ˜ ¯¿Ï·Û·Ó Ù· ·Ô‡ÙÛÈ· ÙÔ˘˜ Î·È ı¤ÏÔ˘Ó Ó· Ù· ¿Ó ÛÙÔÓ ÙÛ·ÁοÚË ÁÈ· Ó· ·ÏÏ¿ÍÔ˘Ó Ù· Ù·ÎÔ‡ÓÈ·. ¶fiÛ· Ù·ÎÔ‡ÓÈ· Ú¤ÂÈ Ó· ÊÙÈ¿ÍÂÈ Ô ÙÛ·ÁοÚ˘;

A¿ÓÙËÛË: O ÙÛ·ÁοÚ˘ Ú¤ÂÈ Ó· ÊÙÈ¿ÍÂÈ ... Ù·ÎÔ‡ÓÈ·. ∫¿ÔÈÔÈ ¿ÏÏÔÈ Ó¿ÓÔÈ ÚÔËÁÔ˘Ì¤Óˆ˜ ›¯·Ó ¿ÂÈ Ù· ·Ô‡ÙÛÈ· ÙÔ˘˜ Î·È ¿ÏÏ·Í·Ó 12 Ù·ÎÔ‡ÓÈ·. ¶fiÛÔÈ ‹Ù·Ó ·˘ÙÔ› ÔÈ Ó¿ÓÔÈ;

A¿ÓÙËÛË: ◊Ù·Ó ... Ó¿ÓÔÈ.

3 ÀÔÏÔÁ›˙ˆ Î·È Û˘ÌÏËÚÒÓˆ ÙÔÓ ·ÚÈıÌfi Ô˘ Ï›ÂÈ.

50 + 30 = ... 30 + ... = 100 90 – 40 = ... 30 + ... = 60 100 – 20 = ... 40 + ... = 90

60 +20 32

20 +50

90 –30

6 + 9 = ... 17 – 8 = ... 14 – 9 = ...

60 –30

80 –40

1. ∑ËÙԇ̠·fi ÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ÌÂÙÚ‹ÛÔ˘Ó ÚÔÊÔÚÈο ·Ó¿ 3 ̤¯ÚÈ ÙÔ 30 Î·È ·Ó¿ 4 ̤¯ÚÈ ÙÔ 40.

Ë

ÂÓfiÙËÙ· 9 ÀÔÏÔÁ›˙ˆ Î·È Áڿʈ Ù· ·ÔÙÂϤÛÌ·Ù· ÙˆÓ ڿ͈Ó.

4

5 °Ú¿Êˆ ÙÔÓ ·ÚÈıÌfi Ô˘ ‚Ú›ÛÎÂÙ·È ÚÈÓ Î·È ÌÂÙ¿.

55 ... 56 57 ... ... 88 ...

... 68 ... ... 99 ...

... 79 ... ... 70 ...

... 91 ... ... 89 ... 6

£¤Ïˆ Ó· ·ÓÙ·ÏϿ͈ ÙÔ ÌÂÁ¿ÏÔ ÓfiÌÈÛÌ· Ì ¿ÏÏ· ÌÈÎÚfiÙÂÚ· ·ÏÏ¿ ›Û˘ Û˘ÓÔÏÈ΋˜ ·Í›·˜. μ¿˙ˆ Û ·ÎÏÔ Ù· ÓÔÌ›ÛÌ·Ù· Ô˘ ÌÔÚÒ Ó· ¿Úˆ.

4. ¶ÚÔÙ›ÓÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÚÔÛı¤ÛÂȘ Î·È ·Ê·ÈÚ¤ÛÂȘ ‰È„‹ÊÈˆÓ ·ÚÈıÌÒÓ Ì¤¯ÚÈ ÙÔ 100, ηٿ ÙȘ Ôԛ˜ Ô ‰Â‡ÙÂÚÔ˜ ·ÚÈıÌfi˜ Â›Ó·È ‰È„‹ÊÈÔ˜ Ì ÛÙÚÔÁÁ˘Ï¤˜ ‰Âο‰Â˜ (.¯. 63 + 20, 94 – 50 Î.Ï.).

33

ªÂ ·fiÊ·ÛË Ù˘ ∂ÏÏËÓÈ΋˜ ∫˘‚¤ÚÓËÛ˘ Ù· ‰È‰·ÎÙÈο ‚È‚Ï›· ÙÔ˘ ¢ËÌÔÙÈÎÔ‡, ÙÔ˘ °˘ÌÓ·Û›Ô˘ Î·È ÙÔ˘ §˘Î›Ԣ Ù˘ÒÓÔÓÙ·È ·fi ÙÔÓ √ÚÁ·ÓÈÛÌfi ∂ΉfiÛˆ˜ ¢È‰·ÎÙÈÎÒÓ μÈ‚Ï›ˆÓ Î·È ‰È·Ó¤ÌÔÓÙ·È ‰ˆÚÂ¿Ó ÛÙ· ¢ËÌfiÛÈ· ™¯ÔÏ›·. Δ· ‚È‚Ï›· ÌÔÚ› Ó· ‰È·Ù›ıÂÓÙ·È ÚÔ˜ ÒÏËÛË, fiÙ·Ó Ê¤ÚÔ˘Ó ‚È‚ÏÈfiÛËÌÔ ÚÔ˜ ·fi‰ÂÈÍË Ù˘ ÁÓËÛÈfiÙËÙ¿˜ ÙÔ˘˜. ∫¿ı ·ÓÙ›Ù˘Ô Ô˘ ‰È·Ù›ıÂÙ·È ÚÔ˜ ÒÏËÛË Î·È ‰Â ʤÚÂÈ ‚È‚ÏÈfiÛËÌÔ, ıˆÚÂ›Ù·È ÎÏ„›Ù˘Ô Î·È Ô ·Ú·‚¿Ù˘ ‰ÈÒÎÂÙ·È Û‡Ìʈӷ Ì ÙȘ ‰È·Ù¿ÍÂȘ ÙÔ˘ ¿ÚıÚÔ˘ 7, ÙÔ˘ ¡fiÌÔ˘ 1129 Ù˘ 15/21 ª·ÚÙ›Ô˘ 1946 (ºEK 1946, 108, Aã).

BIB§IO™HMO

∞·ÁÔÚ‡ÂÙ·È Ë ·Ó··Ú·ÁˆÁ‹ ÔÔÈÔ˘‰‹ÔÙ ÙÌ‹Ì·ÙÔ˜ ·˘ÙÔ‡ ÙÔ˘ ‚È‚Ï›Ô˘, Ô˘ ηχÙÂÙ·È ·fi ‰ÈηÈÒÌ·Ù· (copyright), ‹ Ë ¯Ú‹ÛË ÙÔ˘ Û ÔÔÈ·‰‹ÔÙ ÌÔÚÊ‹, ¯ˆÚ›˜ ÙË ÁÚ·Ù‹ ¿‰ÂÈ· ÙÔ˘ ¶·È‰·ÁˆÁÈÎÔ‡ πÓÛÙÈÙÔ‡ÙÔ˘.